From 7dab6db049b4aae03ab7236bbf603c19ddf45b9d Mon Sep 17 00:00:00 2001 From: joaquinvanschoren Date: Mon, 5 Feb 2024 12:17:43 +0100 Subject: [PATCH] Update documentation --- .DS_Store | Bin 0 -> 6148 bytes _sources/labs/Lab 2 - Tutorial.ipynb | 4 +- genindex.html | 1 + intro.html | 1 + labs/.DS_Store | Bin 0 -> 6148 bytes ...Linear Models for Regression Solution.html | 1116 -------------- ...ar Models for Classification Solution.html | 1079 ------------- labs/Lab 2 - Tutorial.html | 31 +- labs/Lab 2a - Kernelization Solution.html | 1026 ------------- labs/Lab 2b - Model Selection Solution.html | 953 ------------ labs/Lab 3 - Ensembles Solution.html | 1027 ------------- labs/Lab 3b - Ensembles Solution.html | 1146 -------------- labs/Lab 4 - Pipelines Solution.html | 978 ------------ labs/Lab 5 - Bayesian learning Solution.html | 848 ----------- labs/Lab 6 - Neural Networks Solution.html | 900 ----------- ...onvolutional Neural Networks Solution.html | 1272 ---------------- ...b - Neural Networks for text Solution.html | 1332 ----------------- objects.inv | Bin 1467 -> 1467 bytes search.html | 1 + searchindex.js | 2 +- studies/S9 Multi-fidelity optimization.html | 1 + 21 files changed, 33 insertions(+), 11685 deletions(-) create mode 100644 .DS_Store create mode 100644 labs/.DS_Store delete mode 100644 labs/Lab 1a - Linear Models for Regression Solution.html delete mode 100644 labs/Lab 1b - Linear Models for Classification Solution.html delete mode 100644 labs/Lab 2a - Kernelization Solution.html delete mode 100644 labs/Lab 2b - Model Selection Solution.html delete mode 100644 labs/Lab 3 - Ensembles Solution.html delete mode 100644 labs/Lab 3b - Ensembles Solution.html delete mode 100644 labs/Lab 4 - Pipelines Solution.html delete mode 100644 labs/Lab 5 - Bayesian learning Solution.html delete mode 100644 labs/Lab 6 - Neural Networks Solution.html delete mode 100644 labs/Lab 7a - Convolutional Neural Networks Solution.html delete mode 100644 labs/Lab 7b - Neural Networks for text Solution.html diff --git a/.DS_Store b/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..616bbdc39ebb8c79d797e4153c95b00a51a126b5 GIT binary patch literal 6148 zcmeH~F^p-|IIp0@%`>`0}tYV?JQU858c;`(>VPx7mxdj}CZBAF**F#?bS%VAu{EI}48kTuylS)o}@50O}5V74$I-g^3LW{49$8wtT3Tj4Jb$fDX>sr)AP~K|0Dg`{J&^XDg~s# zn<-$!;pedDOXb=6@AbTX%Brs$os7#F9)1Ft_))y0hjG97f~?8b$qG$B0wIHf6nLou EfBT>krvLx| literal 0 HcmV?d00001 diff --git a/_sources/labs/Lab 2 - Tutorial.ipynb b/_sources/labs/Lab 2 - Tutorial.ipynb index de9f87bae..d21c618f0 100644 --- a/_sources/labs/Lab 2 - Tutorial.ipynb +++ b/_sources/labs/Lab 2 - Tutorial.ipynb @@ -8,7 +8,7 @@ } }, "source": [ - "# Lab 3 Tutorial: Model Selection in scikit-learn" + "# Lab 2 Tutorial: Model Selection in scikit-learn" ] }, { @@ -1007,7 +1007,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.10.10" } }, "nbformat": 4, diff --git a/genindex.html b/genindex.html index a5787d2ec..a036e0eca 100644 --- a/genindex.html +++ b/genindex.html @@ -200,6 +200,7 @@ +
  • Lab 2 Tutorial: Model Selection in scikit-learn
  • Lab 4 Tutorial: Data engineering pipelines
  • Lab 6 Tutorial: Deep Learning with TensorFlow
  • Lab 7 Tutorial: Deep Learning for text
    • diff --git a/intro.html b/intro.html index 8f6e4485e..20efe4187 100644 --- a/intro.html +++ b/intro.html @@ -202,6 +202,7 @@ +
  • Lab 2 Tutorial: Model Selection in scikit-learn
  • Lab 4 Tutorial: Data engineering pipelines
  • Lab 6 Tutorial: Deep Learning with TensorFlow
  • Lab 7 Tutorial: Deep Learning for text
    • diff --git a/labs/.DS_Store b/labs/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..5008ddfcf53c02e82d7eee2e57c38e5672ef89f6 GIT binary patch literal 6148 zcmeH~Jr2S!425mzP>H1@V-^m;4Wg<&0T*E43hX&L&p$$qDprKhvt+--jT7}7np#A3 zem<@ulZcFPQ@L2!n>{z**++&mCkOWA81W14cNZlEfg7;MkzE(HCqgga^y>{tEnwC%0;vJ&^%eQ zLs35+`xjp>T0 - - - - - - - - - Lab 1: Linear models — ML Engineering - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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    Lab 1: Linear models

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    Lab 1: Linear models#

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    Part 1: Regression#

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    The NO2 dataset contains 500 measurement of pollution caused by cars. The goal is to predict the concentration of \(NO_2\) from data about traffic and atmospheric conditions. The predictive variables include the number of cars per hour, temperature, wind, and time of day.

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    # Auto-setup when running on Google Colab
-if 'google.colab' in str(get_ipython()):
-    !pip install openml
-
-# General imports
-%matplotlib inline
-import numpy as np
-import pandas as pd
-import matplotlib.pyplot as plt
-import openml as oml
-from matplotlib import cm
-import sys
-import os
-
-# Hide convergence warning for now
-import warnings
-from sklearn.exceptions import ConvergenceWarning
-warnings.filterwarnings("ignore", category=ConvergenceWarning)
-
-# Hiding all warnings. Not recommended, just for compilation.
-if not sys.warnoptions:
-    warnings.simplefilter("ignore")
-    os.environ["PYTHONWARNINGS"] = "ignore"
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    # Download NO2 data. Takes a while the first time.
-no2 = oml.datasets.get_dataset(547)
-X, y, _, _ = no2.get_data(target=no2.default_target_attribute); 
-attribute_names = list(X)
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    Quick visualization#

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    We can use pandas to quickly visualize the data. If you are new to pandas, take some time to understand the code.

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    We’ll remove the ‘day’ feature to focus on the non-temporal aspects of this interaction. We are not aiming to predict future levels, and even if we would it would require special treatment (e.g. different train-test splits). There also doesn’t seem to be a long term trend in the data, even though there are clear periodic trends in temperature.

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    df = pd.DataFrame(X, columns=attribute_names).join(pd.DataFrame(list(y),columns=['target']))
-df = df.sort_values(['day','hour_of_day']).drop('day',axis=1)
-df.plot(use_index=False,figsize=(20,5),cmap=cm.get_cmap('brg'));
-X = X.drop('day',axis=1)
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    df.head()
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    cars_per_hourtemperature_at_2mwind_speedtemperature_diff_2m_25mwind_directionhour_of_daytarget
    427.643008.54.3-0.2322.0133.22287
    207.750618.24.50.2307.0143.15274
    2558.124155.22.80.3209.084.19570
    4887.641086.72.3-0.4247.0103.98155
    948.316306.31.21.3265.0174.14155
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    If we plot the data, ordered by time of measurement, we can see that the wind direction (measured in angular degrees) is scaled very differently from the other features. Let’s now zoom in to the other measures:

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    df.drop('wind_direction',axis=1).plot(use_index=False,figsize=(20,5),cmap=cm.get_cmap('brg'));
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    We can see that the target (\(NO_2\) levels) seem to be correlated to the number of cars per hour, which makes sense because cars produce \(NO_2\). Other influences (air temperature differences and wind) seem to have a more complex and subtle effect. Let’s try to model these using linear regression models.

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    Exercise 1: Model benchmark#

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    It is clear that \(NO_2\) concentrations depend on a combination of these features, so we will now try to learn this complex relationship. We first evaluate a range of linear regression problems, i.e. Linear Regression, Ridge, Lasso and ElasticNet, as well as kNN. Since we observed that somf features have very different scales, we’ll also build pipelines of all these measures with an additional scaling step. For now, we’ll stick to the default hyperparameter settings.

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    Exercise 1.1#

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    Implement a function below which evaluates each classifier passed into it on the given data, and then returns both the train and test scores of each as a list. You are allowed to import additional functions from whichever module you like, but you should be able to complete the function with cross_validate function and standard Python built-ins. Below you the function you will find example output.

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    def evaluate_learners(models, X, y):
-    """     
-    Given a list of models [model1, model2, ..., modelN] return two lists:
-     - a list with the scores obtained on the training samples for each model,
-     - a list with the test scores obtained on the test samples for each model.
-     The order of scores should match the order in which the models were originally provided. E.g.:     
-     [Model1 train score, ..., ModelN train score], [Model1 test score, ..., ModelN test score]
-    """
-    pass
-
-# # Example output:
-# train_scores, test_scores = ([[0.92 , 0.924, 0.916, 0.917, 0.921],  # Model 1 train score for each of 5 folds.
-#                               [0.963, 0.962, 0.953, 0.912, 0.934],  # Model 2 train score for each of 5 folds.
-#                               ..
-#                              [[0.801, 0.811, 0.806, 0.826, 0.804],  # Model 1 test score for each of 5 folds.
-#                               [0.766, 0.756, 0.773, 0.756, 0.741],  # Model 2 test score for each of 5 folds.
-#                               ..
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    Solution#

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    # MODEL IMPLEMENTATION:
-from sklearn.model_selection import cross_validate, train_test_split
-from sklearn.linear_model import LinearRegression, Ridge, Lasso, ElasticNet
-from sklearn.neighbors import KNeighborsRegressor
-from sklearn.pipeline import make_pipeline
-from sklearn.preprocessing import StandardScaler
-
-def evaluate_learners(models, X, y):
-    """ Evaluate each model in 'models' with cross-validation on the provided (X, y) data. 
-    
-    Given a list of models [model1, model2, ..., modelN] return two lists:
-     - a list with the scores obtained on the training samples for each model,
-     - a list with the test scores obtained on the test samples for each model.
-     The order of scores should match the order in which the models were originally provided. E.g.:     
-     [Model1 train score, ..., ModelN train score], [Model1 test score, ..., ModelN test score]
-    """
-    # Evaluate with 5-fold cross-validation.
-    xvals = [cross_validate(m, X, y, return_train_score= True, n_jobs=-1) for m in models]
-    test_scores = [x['test_score'] for x in xvals]
-    train_scores = [x['train_score'] for x in xvals]
-    return train_scores, test_scores
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    Exercise 1.2#

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    Call the function you created with a Linear Regression, Ridge, Lasso and ElasticNet, as well as kNN. -Store the return values in the variables train_scores and test_scores. Then, run the code given below to produce a plot visualizing the scores.

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    # Dummy code. Replace with the actual classifiers and scores
-classifiers = [LinearRegression()]
-train_scores, test_scores = [[0.6,0.7,0.8]], [[0.5,0.6,0.7]]
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    Solution#

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    models = [LinearRegression(), Ridge(), Lasso(), ElasticNet(), KNeighborsRegressor()]
-#models = np.array([m for m in models]).flatten()
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-train_scores, test_scores = evaluate_learners(models, X, y)
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    # Plot a bar chart of the train and test scores of all the classifiers, including the variance as error bars
-# Note: we use some more advanced visualization and formatting tricks here to get a nice plot, but
-# it doesn't have to done this way, as long as the results are the same (or similar)
-fig, ax = plt.subplots(figsize=(10,6))
-width=0.45
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-ax.barh(np.arange(len(train_scores)), np.mean(test_scores, axis=1), width,
-        yerr= np.std(test_scores, axis=1), color='green', label='test R^2')
-ax.barh(np.arange(len(train_scores))-width, np.mean(train_scores, axis=1), width,
-        yerr= np.std(train_scores, axis=1), color='red', label='train R^2')
-for i, te, tr in zip(np.arange(len(train_scores)),test_scores,train_scores):
-    ax.text(0, i, "{:.3f} +- {:.3f}".format(np.mean(te),np.std(te)), color=('white' if np.mean(te)>0.1 else 'black'), va='center')
-    ax.text(0, i-width, "{:.3f} +- {:.3f}".format(np.mean(tr),np.std(tr)), color=('white' if np.mean(tr)>0.1 else 'black'), va='center')
-labels = [c.__class__.__name__ if not hasattr(c, 'steps') else c.steps[0][0] + "_" + c.steps[1][0] for c in models]
-ax.set(yticks=np.arange(len(train_scores))-width/2, yticklabels=labels)
-ax.legend(bbox_to_anchor=(1.05, 1), loc=2)
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-plt.show()
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    -../_images/781c74b09bb62245202394cc3f7edab634155e2ff0fab05676f2bcc1d1b5bb8e.png -
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    Exercise 1.3#

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    Interpret the plot. Which is the best regressor? Are any of the models overfitting? If so, what can we do to solve this? Is there a lot of variance in the results?

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    Solution#

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    Linear regression and ridge regression don’t surpass 0.5 \(R^2\), yet don’t seem to drastically overfit. kNN is drastically overfitting. Lasso and ElasticNet are catastrophically bad in their default settings.

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    Exercise 2: Regularization#

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    We will now tune these algorithm’s main regularization hyperparameter: the regularization hyperparameter (alpha) in Lasso and Ridge, and the number of neighbors (n_neighbors) in kNN.

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    We expect the optimum for the alpha parameters to lie in \([10^{-12},10^{12}]\) and for n_neighbors between 1 and 50. alpha should be varied on a log scale (i.e. [0.01, 0.1, 1, 10, 100]), k should be varied uniformly (i.e. [1,2,3,4]).

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    Exercise 2.1#

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    Vary the hyperparameters in the range given above and, for each regressor, create a line plot that plots both the training and test score for every value of the regularization hyperparameter. Hence, you should produce 3 plots, one for each regressor. Use the default 5-fold cross validation for all scores, but only plot the means.

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    Hints:

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    • Think about the time complexity of these models. Trying too many hyperparameter values may take too much time.

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    • You can make use of numpy’s logspace, geomspace, and linspace functions.

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    • You can use matplotlib’s default plot function to plot the train and test scores.

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    • You can manually loop over the hyperparameter ranges, or you can already check out scikit-learn’s GridSearchCV function to save some programming. We’ll see it again later in the course.

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    Solution#

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    # Design the hyperparameter search space
-from sklearn.model_selection import GridSearchCV
-
-param_a = {'alpha': np.logspace(-12, 12, num=22)}
-param_elastic = {'l1_ratio': np.linspace(0, 1, num=11),
-                 'alpha': np.logspace(-12, 12, num=25)}
-param_k = {'kneighborsregressor__n_neighbors': np.geomspace(1, 60, num=12, dtype=int)[1:]}
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-models = [Ridge(), Lasso(), make_pipeline(StandardScaler(), KNeighborsRegressor()), ElasticNet()]
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-grids = [param_a,param_a,param_k,param_elastic]
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    # Generic plot for 1D grid search
-def plot_tuning(grid_search, param_name, ax):
-    """
-    grid_search: the result of the GridSearchCV
-    param_name: the name of the parameter that is being varied
-    """
-    ax.plot(grid_search.param_grid[param_name], grid_search.cv_results_['mean_test_score'], marker = '.', label = 'Test score')
-    ax.plot(grid_search.param_grid[param_name], grid_search.cv_results_['mean_train_score'], marker = '.', label = 'Train score')
-    ax.set_ylabel('score (ACC)')
-    ax.set_xlabel(param_name)
-    ax.legend(loc='lower left')
-    ax.set_xscale('log')
-    ax.set_title(grid_search.best_estimator_.__class__.__name__)
-    bp, bs = grid_search.best_params_[param_name], grid_search.best_score_
-    ax.text(bp,bs+0.01,"  best:{:.2E}, R2:{:.4f}".format(bp,bs))
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    # Run the grid search
-grid_searches = [GridSearchCV(m,grid,n_jobs=-1, cv=3, return_train_score=True).fit(X,y) for m,grid in zip(models,grids)]
-fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(15,5))
-for grid_search, param, ax in zip(grid_searches[0:3],['alpha','alpha','kneighborsregressor__n_neighbors'],axes):
-    plot_tuning(grid_search, param, ax)
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    Exercise 2.2#

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    Interpret the plots. When are the methods underfitting? When are they overfitting? How sensitive are they to the regularization hyperparameter?

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    Solution#

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    Ridge and Lasso behave very similarly, producing the same optimal result for small alpha’s (small amounts of regularization), and then quickly dropping down to default performance (0 \(R^2\)) around alpha=0.1. Any more regularization makes the model completely underfit the data. The only difference is that Ridge has a slightly more gradual descent than Lasso. kNN yields a worse score (0.4175 \(R^2\)) even after tuning. It has a clear optimum around 9 nearest neighbors, after which it gradually starts underfitting.

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    Exercise 2.3#

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    ElasticNet allows to mix L1 and L2 loss, and the l1_ratio hyperparameter defines the ratio of L1 loss. Hence, it has two interacting hyperparameters: l1_ratio and alpha. Run a grid search to obtain a matrix of l1_ratio and alpha values and the resulting cross-validation scores. Then, use the function provided below to plot a heatmap of all values and interpret the result. Can you explain how the two hyperparameters interact?

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    # Generic heatmap
-def heatmap(values, xlabel, ylabel, xticklabels, yticklabels, cmap=None,
-            vmin=None, vmax=None, ax=None, fmt="%0.2f", printvalues=False):
-    """
-    Plots a heatmap for the performance of a model for every combination of two hyperparameter values
-    
-    values: nxn array with all evaluation results, varying the first hyperparameter first
-    xlabel: name of the first hyperparameter
-    ylabel: name of the second hyperparameter
-    xticklabels: values of the first hyperparameter
-    yticklabels: values of the second hyperparameter
-    cmap: colormap
-    vmin: minimal score
-    vmax: maximal score
-    ax: plot axes
-    fmt: format for printing the scores
-    printvalues: whether to print the scores
-    """
-    if ax is None:
-        ax = plt.gca()
-    img = ax.pcolor(values, cmap=cmap, vmin=None, vmax=None)
-    img.update_scalarmappable()
-    ax.set_xlabel(xlabel, fontsize=10)
-    ax.set_ylabel(ylabel, fontsize=10)
-    ax.set_xticks(np.arange(len(xticklabels)) + .5)
-    ax.set_yticks(np.arange(len(yticklabels)) + .5)
-    ax.set_xticklabels(xticklabels)
-    ax.set_yticklabels(yticklabels)
-    ax.set_aspect(1)
-    
-    ax.tick_params(axis='y', labelsize=12)
-    ax.tick_params(axis='x', labelsize=12, labelrotation=90)
-
-    if(printvalues):
-        for p, color, value in zip(img.get_paths(), img.get_facecolors(), img.get_array()):
-            x, y = p.vertices[:-2, :].mean(0)
-            if np.mean(color[:3]) > 0.5:
-                c = 'k'
-            else:
-                c = 'w'
-            ax.text(x, y, fmt % value, color=c, ha="center", va="center", size=10)
-    return img
-
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    Solution#

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    scores = np.array(pd.DataFrame(grid_searches[3].cv_results_).mean_test_score).reshape(25, 11).T
-plt.rcParams.update({'font.size': 12})
-fig, axes = plt.subplots(1, 1, figsize=(13, 13))
-heatmap(scores, xlabel='alpha', xticklabels=list(map(lambda n: "%.E" % n, param_elastic['alpha'])),
-        ylabel='l1_ratio', yticklabels=np.around(param_elastic['l1_ratio'],4), cmap="viridis", fmt="%.2f", ax=axes);
-
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    -../_images/e154775f48abf02a54e1f4c4ae85e99db588736b7150af1cf743b47d0cd9367f.png -
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    For ElasticNet we see the same sudden drop in performance around alpha=0.1. For l1_ratio=0, it is identical to Ridge (L2), showing a more gradual descent. For l1_ration=1, it is identical to Lasso (L1), showing the same sharp performance drop.

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    Exercise 3: Visualizing coefficients#

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    Finally, let’s verify whether the different optimized linear models also find the same coefficients.

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    Exercise 3.1#

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    Draw a scatterplot plotting the coefficients of the different models in different colors. Do you see much difference between the different models?

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    For all models, choose an alpha parameter that seems to work well in the previous exercise. When in doubt, use alpha=0.001.

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    Solution#

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    def scatter_coefficients(alpha=0.001):
-    models = [LinearRegression(), Ridge(alpha=alpha), Lasso(alpha=alpha), ElasticNet(alpha=alpha)]
-    coeff = [m.fit(X,y).coef_ for m in models]
-    attribute_names = list(X)
-
-    col = ['k','b','r','y']
-    plt.figure()
-    plt.xticks(rotation=45,ha="right")
-    for i in range(0,4):
-        plt.scatter(attribute_names, coeff[i], s=(4-i)*40, c=col[i], label=models[i].__class__.__name__)
-    plt.legend();
-scatter_coefficients(alpha=0.001)
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    -../_images/3eae0847f567c3e0d9a63422cc8dc1e08403db76ec4296c68ee7251a60951631.png -
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    The different techniques find almost exactly the same coefficients (the markers overlap). cars_per_hour is the most influential, followed by temperature_diff_2m_25m and wind_speed. The others are nearly zero.

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    Exercise 3.2#

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    Redraw the same plot but now using a large amount of regularization (e.g. alpha=1). What do you observe? Does this help you explain the performance difference between Ridge and Lasso in exercise 1.2?

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    Solution#

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    Increasing alpha makes Lasso completely ignore most features: the coefficients are exactly 0. Hence, it is important to tune alpha carefully.

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    scatter_coefficients(alpha=1)
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    -By Joaquin Vanschoren -

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    Lab 1: Linear models

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    Lab 1: Linear models#

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    Part 2: Classification#

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    The Fashion-MNIST dataset contains 70,000 images of Zalando fashion products, classified into 10 types of clothing, each represented by 28 by 28 pixel values. We’s see how well we can classify these with linear models. Let’s start with looking at our data:

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    # Auto-setup when running on Google Colab
-if 'google.colab' in str(get_ipython()):
-    !pip install openml
-
-# General imports
-%matplotlib inline
-import numpy as np
-import pandas as pd
-import matplotlib.pyplot as plt
-import openml as oml
-from matplotlib import cm
-
-# Hide convergence warning for now
-import warnings
-from sklearn.exceptions import ConvergenceWarning
-warnings.filterwarnings("ignore", category=ConvergenceWarning)
-
-# Hiding all warnings. Not recommended, just for compilation.
-if not sys.warnoptions:
-    warnings.simplefilter("ignore")
-    os.environ["PYTHONWARNINGS"] = "ignore"
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    # Download FMINST data. Takes a while the first time.
-fmnist = oml.datasets.get_dataset(40996)
-X, y, _, _ = fmnist.get_data(target=fmnist.default_target_attribute); 
-fmnist_classes = {0:"T-shirt/top", 1: "Trouser", 2: "Pullover", 3: "Dress", 4: "Coat", 5: "Sandal", 
-                  6: "Shirt", 7: "Sneaker", 8: "Bag", 9: "Ankle boot"}
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    # Take some random examples, reshape to a 32x32 image and plot
-from random import randint
-fig, axes = plt.subplots(1, 5,  figsize=(10, 5))
-for i in range(5):
-    n = randint(0,70000)
-    axes[i].imshow(X.values[n].reshape(28, 28), cmap=plt.cm.gray_r)
-    axes[i].set_xlabel((fmnist_classes[int(y.values[n])]))
-    axes[i].set_xticks(()), axes[i].set_yticks(())
-plt.show();
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    -../_images/8bfb28f81299c513ee0ba1ae8d4d8170474fb110d8e57c976b472b22d950aaa1.png -
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    Exercise 1: A quick benchmark#

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    First, we’ll try the default Logistic Regression and Linear SVMs. Click the links to read the documentation. We’ll also compare it to k-Nearest Neighbors as a point of reference. To see whether our models are overfitting, we also evaluate the training set error. This can be done using cross_validate instead of cross_val_scores.

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    For now we are just interested in a quick approximation, so we don’t use the full dataset for our experiments. Instead, we use 10% of our samples:

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    from sklearn.model_selection import train_test_split, cross_validate
-from sklearn.linear_model import LogisticRegression
-from sklearn.svm import LinearSVC
-from sklearn.neighbors import KNeighborsClassifier
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-# Take a 10% stratified subsample to speed up experimentation
-Xs, _, ys, _ = train_test_split(X,y, stratify=y, train_size=0.1)
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    With this small sample of our data we can now train and evaluate the three classifiers.

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    Exercise 1.1#

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    Implement a function below which evaluates each classifier passed into it on the given data, and then returns both the train and test scores of each as a list. You are allowed to import additional functions from whichever module you like, but you should be able to complete the function with cross_validate function and standard Python built-ins. Below the function you will find example output.

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    def evaluate_learners(classifiers, X, y):
-    """ Evaluate each classifier in 'classifiers' with cross-validation on the provided (X, y) data. 
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-    Given a list of scikit-learn classifiers [Classifier1, Classifier2, ..., ClassifierN] return two lists:
-     - a list with the scores obtained on the training samples for each classifier,
-     - a list with the test scores obtained on the test samples for each classifier.
-     The order of scores should match the order in which the classifiers were originally provided. E.g.:     
-     [Classifier1 train score, ..., ClassifierN train score], [Classifier1 test score, ..., ClassifierN test score]
-    """
-    pass
-
-# # Example output:
-# train_scores, test_scores = ([[0.92 , 0.924, 0.916, 0.917, 0.921],  # Classifier 1 train score for each of 5 folds.
-#                               [0.963, 0.962, 0.953, 0.912, 0.934],  # Classifier 2 train score for each of 5 folds.
-#                               [0.867, 0.868, 0.865, 0.866, 0.866]], # Classifier 3 train score for each of 5 folds.
-#                              [[0.801, 0.811, 0.806, 0.826, 0.804],  # Classifier 1 test score for each of 5 folds.
-#                               [0.766, 0.756, 0.773, 0.756, 0.741],  # Classifier 2 test score for each of 5 folds.
-#                               [0.804, 0.814, 0.806, 0.821, 0.806]]) # Classifier 3 test score for each of 5 folds.
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    Solution#

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    # MODEL IMPLEMENTATION:
-def evaluate_learners(classifiers, X, y):
-    """ Evaluate each classifier in 'classifiers' with cross-validation on the provided (X, y) data. 
-    
-    Given a list of classifiers [Classifier1, Classifier2, ..., ClassifierN] return two lists:
-     - a list with the scores obtained on the training samples for each classifier,
-     - a list with the test scores obtained on the test samples for each classifier.
-     The order of scores should match the order in which the classifiers were originally provided. E.g.:     
-     [Classifier1 train scores, ..., ClassifierN train scores], [Classifier1 test scores, ..., ClassifierN test scores]
-    """
-    # Evaluate with 3-fold cross-validation.
-    xvals = [cross_validate(clf, X, y, return_train_score= True, n_jobs=-1) for clf in classifiers]
-    train_scores = [x['train_score'] for x in xvals]
-    test_scores = [x['test_score'] for x in xvals]
-    return train_scores, test_scores
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    Exercise 1.2#

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    Call the function you created with a Logistic Regression, Linear SVM, and k-Nearest Neighbors Classifier. -Store the return values in the variables train_scores and test_scores. Then, run the code given below to produce a plot visualizing the scores.

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    # Dummy code. Replace with the actual classifiers and scores
-classifiers = [LogisticRegression()]
-train_scores, test_scores = [[0.6,0.7,0.8]], [[0.5,0.6,0.7]]
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    Solution#

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    classifiers = [LogisticRegression(), LinearSVC(), KNeighborsClassifier()]
-train_scores, test_scores = evaluate_learners(classifiers, Xs, ys)
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    # Plot a bar chart of the train and test scores of all the classifiers, including the variance as error bars
-fig, ax = plt.subplots()
-width=0.3
-ax.barh(np.arange(len(train_scores)), np.mean(test_scores, axis=1), width,
-        yerr= np.std(test_scores, axis=1), color='green', label='test')
-ax.barh(np.arange(len(train_scores))-width, np.mean(train_scores, axis=1), width,
-        yerr= np.std(train_scores, axis=1), color='red', label='train')
-for i, te, tr in zip(np.arange(len(train_scores)),test_scores,train_scores):
-    ax.text(0, i, "{:.4f} +- {:.4f}".format(np.mean(te),np.std(te)), color='white', va='center')
-    ax.text(0, i-width, "{:.4f} +- {:.4f}".format(np.mean(tr),np.std(tr)), color='white', va='center')
-ax.set(yticks=np.arange(len(train_scores))-width/2, yticklabels=[c.__class__.__name__ for c in classifiers])
-ax.set_xlabel('Accuracy')
-ax.legend(bbox_to_anchor=(1.05, 1), loc=2)
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-plt.show()
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    -../_images/504d0e079df9858798d9ebfd8fab47494b5a288f9205ee5bd9e7efef32504a5a.png -
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    Exercise 1.3#

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    Interpret the plot. Which is the best classifier? Are any of the models overfitting? If so, what can we do to solve this? Is there a lot of variance in the results?

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    Solution#

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    k-NN and LogisticRegression have the best cross-validated test set performance. The linear SVM performs noticeably worse. Both linear models have a big difference between training set accuracy and test set accuracy. This indicates that both linear models are likely overfitted and need to be regularized. The standard deviation of the results is very small: the error bars are hardly noticeable.

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    Exercise 2: Regularization#

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    We will now tune these algorithm’s main regularization hyperparameter: the misclassification cost in SVMs (C), the regularization parameter in logistic regression (C), and the number of neighbors (n_neighbors) in kNN. We expect the optimum for the C parameters to lie in \([10^{-12},10^{12}]\) and for n_neighbors between 1 and 50. C should be varied on a log scale (i.e. [0.01, 0.1, 1, 10, 100]) and k should be varied uniformly (i.e. [1,2,3,4]).

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    Exercise 2.1#

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    Vary the regularization parameters in the range given above and, for each classifier, create a line plot that plots both the training and test score for every value of the regularization hyperparameter. Hence, you should produce 3 plots, one for each classifier. Use the default 5-fold cross validation for all scores, but only plot the means.

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    Hints:

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    • Think about the time complexity of these models. Trying too many hyperparameter values may take too much time.

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    • You can make use of numpy’s logspace, geomspace, and linspace functions.

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    • You can use matplotlib’s default plot function to plot the train and test scores.

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    • You can manually loop over the hyperparameter ranges, or you can already check out scikit-learn’s GridSearchCV function to save some programming. We’ll see it again later in the course.

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    Solution#

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    from sklearn.model_selection import GridSearchCV
-
-param_c = {'C': np.logspace(-12, 12, num=22)}
-param_k = {'n_neighbors': np.geomspace(1, 60, num=12, dtype=int)[1:]}
-grids = [param_c, param_c, param_k]
-grid_searches = [GridSearchCV(clf, grid, n_jobs=-1, cv=3, return_train_score=True).fit(Xs, ys) for clf,grid in zip(classifiers,grids)]
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    # Generic plot for 1D grid search
-# grid_search: the result of the GridSearchCV
-# param_name: the name of the parameter that is being varied
-def plot_tuning(grid_search, param_name, ax):
-    ax.plot(grid_search.param_grid[param_name], grid_search.cv_results_['mean_test_score'], marker = '.', label = 'Test score')
-    ax.plot(grid_search.param_grid[param_name], grid_search.cv_results_['mean_train_score'], marker = '.', label = 'Train score')
-    ax.set_ylabel('score (ACC)')
-    ax.set_xlabel(param_name)
-    ax.legend()
-    ax.set_xscale('log')
-    ax.set_title(grid_search.best_estimator_.__class__.__name__)
-    bp, bs = grid_search.best_params_[param_name], grid_search.best_score_
-    ax.text(bp,bs,"  C:{:.2E}, ACC:{:.4f}".format(bp,bs))
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    fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(15,5))
-for grid_search, param, ax in zip(grid_searches,['C','C','n_neighbors'],axes):
-    plot_tuning(grid_search, param, ax)
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    Exercise 2.2#

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    Interpret the plots. When are the methods underfitting? When are they overfitting? How sensitive are they to the regularization hyperparameter?

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    Solution#

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    We find that, when properly regularized, the linear models both outperform kNN, and that linear SVMs seem to do slighty better of these two. Logistic regression underfits for small values of C, reaches an optimum around C=1e-7, and then starts overfitting. The linear SVM behaves the same way, but with an optimum around C=1e-8. The kNN overfits for small numbers of neighbors, reaches an optimum around n_neighbors=4, and then starts underfitting gradually. Note that these results were obtained on a 10% subsample. Results may be different when we optimize our models on the entire datset.

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    Exercise 3: Interpreting misclassifications#

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    Chances are that your models are not yet perfect. It is important to understand what kind of errors it still makes. Let’s take a closer look at which instances are misclassified and which classes are often confused. -Train the logistic regression model with C=1e-7. Train the model on a training set, and make predictions for a test set (both sets should be sampled from our 10% subsample).

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    # Create a stratified train-test split on a sample
-X_train, X_test, y_train, y_test = train_test_split(Xs,ys, stratify=ys, random_state=0)
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    Exercise 3.1#

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    Train the classifier as described above, obtain the predictions y_pred on the test set, and identify all the misclassified samples misclassified_samples. Then, run the visualization code below to study the misclassifications

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    # Implement the code to obtain the actual predictions on the test set
-y_pred = list(y_test) # dummy values, replace y_test with the actual predictions
-
-# Implement the code to obtain the indices of the misclassified samples
-# Example output:
-# misclassified_samples = [  11,   12,   14,   23,   30,   34,   39,   46,   50,   52,   55]
-misclassified_samples = [0,1,2,3,4] # dummy values
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    Solution#

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    # model implementation:
-model = LogisticRegression(C=1e-7).fit(X_train,y_train)
-y_pred = model.predict(X_test)
-misclassified_samples = np.nonzero(y_pred != list(y_test))[0]
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    # Visualize the (first five) misclassifications, together with the predicted and actual class
-fig, axes = plt.subplots(1, 5,  figsize=(10, 5))
-for nr, i in enumerate(misclassified_samples[:5]):
-    axes[nr].imshow(X_test.values[i].reshape(28, 28), cmap=plt.cm.gray_r)
-    axes[nr].set_xlabel("Predicted: %s,\n Actual : %s" % (fmnist_classes[int(y_pred[i])],fmnist_classes[int(y_test.values[i])]))
-    axes[nr].set_xticks(()), axes[nr].set_yticks(())
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-plt.show();
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    -../_images/6bc401d727123b6bd87d2eae0a74051b5abe968b54ffea3c15b0ca2abd01fefb.png -
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    Exercise 3.2#

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    Interpret the results. Are these misclassifications to be expected?

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    Solution#

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    Some of these seem quite common mistakes, such as confusing shirts and coats. The images are quite coarse so there may not be enough detail. Others, like misclassifying a dress for a t-shirt, seem more curious.

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    Exercise 3.3.#

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    Run the code below on your results to draw the complete confusion matrix and get more insight on the systematic misclassifications -of your model. A confusion matrix shows the amount of examples in for each pair of true and predicted classes. Interpret the results. -Does your model produce certain types of error more often than other types?

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    from sklearn.metrics import confusion_matrix
-cm = confusion_matrix(y_test,y_pred)
-fig, ax = plt.subplots()
-im = ax.imshow(cm)
-ax.set_xticks(np.arange(10)), ax.set_yticks(np.arange(10))
-ax.set_xticklabels(list(fmnist_classes.values()), rotation=45, ha="right")
-ax.set_yticklabels(list(fmnist_classes.values()))
-ax.set_ylabel('True')
-ax.set_xlabel('Predicted')
-for i in range(100):
-    ax.text(int(i/10),i%10,cm[i%10,int(i/10)], ha="center", va="center", color="w")
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    -../_images/8271957e8718704684fe9802943ab20fb59a343bef08445940c61fb3edfcc27f.png -
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    Solution#

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    We see that some categories are much easier to predict than others. For instance, trousers and bags are almost always predicted correctly, while sneakers are occasionally confused with sandals or boots. Shirts, on the other hand, are misclassified close to half of the time, predominantly confused with t-shirts, pullovers, and coats.

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    Exercise 4: Interpreting model parameters#

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    Finally, we’ll take a closer look at the model parameters, i.e. the coefficients of our linear models. Since we are dealing with 28x28 pixel images, we have to learn 784 coefficients. What do these coefficients mean? We’ll start by plotting them as 28x28 pixel images.

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    Exercise 4.1#

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    Train a Logistic Regression model and a Linear SVM using their tuned hyperparameters from exercise 2. -When in doubt, use C=1e-7 for LogReg and C=1e-8 for the SVM. -Pass the trained model to the provided plotting function. Interpret the results in detail. -Why do you get multiple plots per model? What do the features represent in your data. -Does it seems like the models pay attention to the right features? -Do you models seem to ignore certain features? Do you observe differences in quality between the different classes? Do you observe any differences between the models?

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    # Plots the coefficients of the given model as 28x28 heatmaps. 
-# The `name` attribute is optional, it is simply a title for the produced figure
-def plot_coefficients(model, name=None):
-    fig, axes = plt.subplots(1,10,figsize=(20,2))
-    fig.suptitle(name if name else model.__class__.__name__)
-    for i, ax in enumerate(axes):
-        m = ax.imshow(model.coef_[i].reshape(28,28))
-        ax.set_xlabel(fmnist_classes[i])
-        ax.set_xticks(()), ax.set_yticks(())
-    fig.colorbar(m, ax=axes.ravel().tolist())
-
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    Solution#

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    plot_coefficients(LogisticRegression(C=1e-7).fit(X_train,y_train))
-plot_coefficients(LinearSVC(C=1e-8).fit(X_train,y_train))
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    -../_images/80a11a2c179e5f8a77522c05f4f422468c7774b7d3b717ac4d9138733282deb4.png -../_images/5fd4a64c07608758b6297389dbe7fb7e083e227fac06019b39d123a29001f0f3.png -
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    Remember that linear models are typically binary classifiers. They will solve multi-class problems in a one-vs-all approach. Hence, for a 10-class problem, they will build 10 models, each one trained to predict whether an instance is from a specific class or not. This leads to 10 sets of 784 trained coefficients. Above, we plot them as 28x28 matrices, such that each coefficient is plotted at the location of their corresponding pixel value.

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    Very high values for coefficients (bright pixels in the images) or very low values (dark pixels in the images) -cause the corresponding pixel values to have a large effect on the final prediction. In other words, the very bright and very dark pixels in the images are the pixels that the model is mainly ‘looking’ at to make a prediction. We can easily recognize the shapes of the fashion items for each class. For instance, for classifying a t-shirt (yes or no), the model will blow up the pixel values near the edges of the shirt, and especially near the shoulders, while it will suppress the background pixel values near the outlines of the shirt. If the sum of all these values is large, it will likely lead to a positive prediction for that class.

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    We can also see that some classes are less defined than others in these images, and these are typically the classes which are easily confused for other classes.

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    Both models seem to focus on the same coefficients, yielding very similar images, yet smoother for the SVM. Moreover, the Linear SVM uses much smaller coefficients.

    -

    Finally, out of curiosity, let’s see the result of underfitting and overfitting on the learned coefficients:

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    Exercise 4.2#

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    Repeat the previous exercise, but now only with logistic regression. In addition to a tuned version, also add a model that overfits a lot and one that underfits a lot. Interpret and explain the results.

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    Solution#

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    plot_coefficients(LogisticRegression(C=1e-12).fit(X_train,y_train),"Underfitting logistic regression")
-plot_coefficients(LogisticRegression(C=1e-7).fit(X_train,y_train),"Good fit logistic regression")
-plot_coefficients(LogisticRegression(C=1e+10).fit(X_train,y_train),"Overfitting logistic regression")
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    -../_images/6efa631380b4d735e8baac1324069c5b6cc85e79c9aefb1cf59ca5bfb79920f4.png -../_images/5b2d9c856db975415441a705b307a1a95ea90ec9e3a900fc1e6660bdb2afc73b.png -../_images/9be552872fc073adbe897624a3ba5d60378affd323b34ddfcfb44bb3919878a5.png -
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    In the case that we underfit the logistic regression model, we see that the model has very strong believes of the shapes. This is evidenced by the many extreme weights (very bright or very dark). In the underfit model a t-shirt has, in addition to the short sleeves, a heigh weight for the bottom of the t-shirt. With the better tuned model (in the middle), the importance of the overall shape is still present, but the emphasis is on just the short sleeves.

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    If we overfit the model, it pays attention to seemingly random pixels, including pixels that are simply background pixels. The coefficients are much higher (or much more negative), meaning that the model can yield different predictions for only slight variations in the input pixel value.

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    We can expect similar behavior from under- or overfitted linear SVMs.

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    - -
    -
    - Contents -
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    -
    -
    -
    - -
    - -

    -By Joaquin Vanschoren -

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    - - © Copyright 2023. CC0 Licensed - Use as you like. Appropriate credit is very welcome. -
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    - - \ No newline at end of file diff --git a/labs/Lab 2 - Tutorial.html b/labs/Lab 2 - Tutorial.html index 00f09b1f2..71aa2bf52 100644 --- a/labs/Lab 2 - Tutorial.html +++ b/labs/Lab 2 - Tutorial.html @@ -9,7 +9,7 @@ - Lab 3 Tutorial: Model Selection in scikit-learn — ML Engineering + Lab 2 Tutorial: Model Selection in scikit-learn — ML Engineering @@ -65,6 +65,8 @@ + + @@ -187,7 +189,7 @@
  • Lab 8: AutoML

    • Tutorials

    -
      +
      • Python for data analysis
      • Python for scientific computing
      • Machine Learning in Python
        • @@ -201,6 +203,7 @@ +
      • Lab 2 Tutorial: Model Selection in scikit-learn
      • Lab 4 Tutorial: Data engineering pipelines
      • Lab 6 Tutorial: Deep Learning with TensorFlow
      • Lab 7 Tutorial: Deep Learning for text
        • @@ -418,7 +421,7 @@
        -

        Lab 3 Tutorial: Model Selection in scikit-learn

        +

        Lab 2 Tutorial: Model Selection in scikit-learn

        @@ -463,8 +466,8 @@

        Contents

        -
        -

        Lab 3 Tutorial: Model Selection in scikit-learn#

        +
        +

        Lab 2 Tutorial: Model Selection in scikit-learn#

        # General imports
@@ -1166,6 +1169,24 @@ 
        Random Search
                   
 
        
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        previous
        
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        Lab 1: Machine Learning with Python
        
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        next
        
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        Lab 4 Tutorial: Data engineering pipelines
        
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+            
 
        
                 
               
diff --git a/labs/Lab 2a - Kernelization Solution.html b/labs/Lab 2a - Kernelization Solution.html
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-    Lab 2a: Tuning Support Vector Machines — ML Engineering
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        Lab 2a: Tuning Support Vector Machines
        
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        Lab 2a: Tuning Support Vector Machines#
        
-
        Support Vector Machines are powerful methods, but they also require careful tuning. We’ll explore SVM kernels and hyperparameters on an artificial dataset. We’ll especially look at model underfitting and overfitting.
        
-
        
-
        
-
        # Auto-setup when running on Google Colab
-if 'google.colab' in str(get_ipython()):
-    !pip install openml
-
-# General imports
-%matplotlib inline
-import numpy as np
-import pandas as pd
-import matplotlib.pyplot as plt
-import openml as oml
-from matplotlib import cm
-
-# Hide convergence warning for now
-import warnings
-from sklearn.exceptions import ConvergenceWarning
-warnings.filterwarnings("ignore", category=ConvergenceWarning)
-
-# Hiding all warnings. Not recommended, just for compilation.
-if not sys.warnoptions:
-    warnings.simplefilter("ignore")
-    os.environ["PYTHONWARNINGS"] = "ignore"
-
        
-
        
-
        
-
        
-
        
-
        Getting the data#
        
-
        We fetch the Banana data from OpenML: https://www.openml.org/d/1460
        
-
        
-
        
-
        bananas = oml.datasets.get_dataset(1460) # Banana data has OpenML ID 1460
-X, y, _, _ = bananas.get_data(target=bananas.default_target_attribute, dataset_format='array');
-
        
-
        
-
        
-
        
-
        Quick look at the data:
        
-
        
-
        
-
        plt.scatter(X[:,0], X[:,1], c=y,cmap=plt.cm.bwr, marker='.');
-
        
-
        
-
        
-
        
-../_images/694b1c75f3c9d3601c2c41259111616112d476009e17c5ddc523ff74ff7f7057.png
-
        
-
        
-
        
-
        
-
        # Plotting helpers. Based loosely on https://github.com/amueller/mglearn
-def plot_svm_kernel(X, y, title, support_vectors, decision_function, dual_coef=None, show=True):
-    """
-    Visualizes the SVM model given the various outputs. It plots:
-    * All the data point, color coded by class: blue or red
-    * The support vectors, indicated by circling the points with a black border. 
-      If the dual coefficients are known (only for kernel SVMs) if paints support vectors with high coefficients darker
-    * The decision function as a blue-to-red gradient. It is white where the decision function is near 0.
-    * The decision boundary as a full line, and the SVM margins (-1 and +1 values) as a dashed line
-    
-    Attributes:
-    X -- The training data
-    y -- The correct labels
-    title -- The plot title
-    support_vectors -- the list of the coordinates of the support vectores
-    decision_function - The decision function returned by the SVM
-    dual_coef -- The dual coefficients of all the support vectors (not relevant for LinearSVM)
-    show -- whether to plot the figure already or not
-    """
-    # plot the line, the points, and the nearest vectors to the plane
-    #plt.figure(fignum, figsize=(5, 5))
-    plt.title(title)
-    plt.scatter(X[:, 0], X[:, 1], c=y, zorder=10, cmap=plt.cm.bwr, marker='.')
-    if dual_coef is not None:
-        plt.scatter(support_vectors[:, 0], support_vectors[:, 1], c=dual_coef[0, :],
-                    s=70, edgecolors='k', zorder=10, marker='.', cmap=plt.cm.bwr)
-    else:
-        plt.scatter(support_vectors[:, 0], support_vectors[:, 1], facecolors='none',
-                    s=70, edgecolors='k', zorder=10, marker='.', cmap=plt.cm.bwr)
-    plt.axis('tight')
-    x_min, x_max = -3.5, 3.5
-    y_min, y_max = -3.5, 3.5
-
-    XX, YY = np.mgrid[x_min:x_max:300j, y_min:y_max:300j]
-    Z = decision_function(np.c_[XX.ravel(), YY.ravel()])
-
-    # Put the result into a color plot
-    Z = Z.reshape(XX.shape)
-    plt.contour(XX, YY, Z, colors=['k', 'k', 'k'], linestyles=['--', '-', '--'],
-                levels=[-1, 0, 1])
-    plt.pcolormesh(XX, YY, Z, vmin=-1, vmax=1, cmap=plt.cm.bwr, alpha=0.1)
-
-    plt.xlim(x_min, x_max)
-    plt.ylim(y_min, y_max)
-    
-    plt.xticks(())
-    plt.yticks(())
-
-    if show:
-        plt.show()
-    
-def heatmap(values, xlabel, ylabel, xticklabels, yticklabels, cmap=None,
-            vmin=None, vmax=None, ax=None, fmt="%0.2f"):
-    """
-    Visualizes the results of a grid search with two hyperparameters as a heatmap.
-    Attributes:
-    values -- The test scores
-    xlabel -- The name of hyperparameter 1
-    ylabel -- The name of hyperparameter 2
-    xticklabels -- The values of hyperparameter 1
-    yticklabels -- The values of hyperparameter 2
-    cmap -- The matplotlib color map
-    vmin -- the minimum value
-    vmax -- the maximum value
-    ax -- The figure axes to plot on
-    fmt -- formatting of the score values
-    """
-    if ax is None:
-        ax = plt.gca()
-    # plot the mean cross-validation scores
-    img = ax.pcolor(values, cmap=cmap, vmin=None, vmax=None)
-    img.update_scalarmappable()
-    ax.set_xlabel(xlabel, fontsize=10)
-    ax.set_ylabel(ylabel, fontsize=10)
-    ax.set_xticks(np.arange(len(xticklabels)) + .5)
-    ax.set_yticks(np.arange(len(yticklabels)) + .5)
-    ax.set_xticklabels(xticklabels)
-    ax.set_yticklabels(yticklabels)
-    ax.set_aspect(1)
-    
-    ax.tick_params(axis='y', labelsize=12)
-    ax.tick_params(axis='x', labelsize=12, labelrotation=90)
-
-    for p, color, value in zip(img.get_paths(), img.get_facecolors(), img.get_array()):
-        x, y = p.vertices[:-2, :].mean(0)
-        if np.mean(color[:3]) > 0.5:
-            c = 'k'
-        else:
-            c = 'w'
-        ax.text(x, y, fmt % value, color=c, ha="center", va="center", size=10)
-    return img
-
        
-
        
-
        
-
        
-
        
-
        
-
        Exercise 1: Linear SVMs#
        
-
        First, we’ll look at linear SVMs and the different outputs they produce. Check the documentation of LinearSVC
        
-
        The most important inputs are:
        
-
          
-
        • C – The C hyperparameter controls the misclassification cost and therefore the amount of regularization. Lower values correspond to more regularization
          • 
-
        • loss - The loss function, typically ‘hinge’ or ‘squared_hinge’. Squared hinge is the default. Normal hinge is less strict.
          • 
-
        • dual – Whether to solve the primal optimization problem or the dual (default). The primal is recommended if you have many more data points than features (although our datasets is very small, so it won’t matter much).
          • 
-
        
-
        The most important outputs are:
        
-
          
-
        • decision_function - The function used to classify any point. In this case on linear SVMs, this corresponds to the learned hyperplane, or \(y = \mathbf{wX} + b\). It can be evaluated at every point, if the result is positive the point is classified as the positive class and vice versa.
          • 
-
        • coef_ - The model coefficients, i.e. the weights \(\mathbf{w}\)
          • 
-
        • intercept_ - the bias \(b\)
          • 
-
        
-
        From the decision function we can find which points are support vectors and which are not: the support vectors are all
-the points that fall inside the margin, i.e. have a decision value between -1 and 1, or that are misclassified. Also see the lecture slides.
        
-
        
-
        Exercise 1.1: Linear SVMs#
        
-
        Train a LinearSVC with C=0.001 and hinge loss. Then, use the plotting function plot_svm_kernel to plot the results. For this you need to extract the support vectors from the decision function. There is a hint below should you get stuck.
-Interpret the plot as detailed as you can. Afterwards you can also try some different settings. You can also try using the primal instead of the dual optimization problem (in that case, use squared hinge loss).
        
-
        
-
        
-
        # Hint: how to compute the support vectors from the decision function (ignore if you want to solve this yourself)
-# support_vector_indices = np.where((2 * y - 1) * clf.decision_function(X) <= 1)[0]
-# support_vectors = X[support_vector_indices]
-
-# Note that we can also calculate the decision function manually with the formula y = w*X
-# decision_function = np.dot(X, clf.coef_[0]) + clf.intercept_[0]
-
        
-
        
-
        
-
        
-
        
-
        Solution#
        
-
        
-
        
-
        plt.rcParams['figure.dpi'] = 200 # Make figures a bit bigger
-
-from sklearn.svm import LinearSVC
-clf1_1 = LinearSVC(C=0.001, loss='hinge')
-clf1_1.fit(X, y)
-
-support_vector_indices = np.where((2 * y - 1) * clf1_1.decision_function(X) <= 1)[0]
-support_vectors = X[support_vector_indices]
-
-plot_svm_kernel(X, y, "Linear SVM",support_vectors,clf1_1.decision_function)
-
        
-
        
-
        
-
        
-../_images/83c1ed94f8db18fe2a76a7ad8ee05e6d57d615bb2311bfd8c135c9962c89d60e.png
-
        
-
        
-
        Interpretation: As expected, the data cannot be fitted well with a linear SVM. Almost all points fall within the margin. Almost all points are support vectors, except for a few blue points on the top right. The accuracy is only 57%.
        
-
        
-
        
-
        
-
        
-
        Exercise 2: Kernelized SVMs#
        
-
        Check the documentation of SVC
        
-
        It has a few more inputs. The most important:
        
-
          
-
        • kernel - It must be either ‘linear’, ‘poly’, ‘rbf’, ‘sigmoid’, or your custom defined kernel.
          • 
-
        • gamma - The kernel width of the rbf (Gaussian) kernel. Smaller values mean wider kernels.
-Only relevant when selecting the rbf kernel.
          • 
-
        • degree - The degree of the polynomial kernel. Only relevant when selecting the poly kernel.
          • 
-
        
-
        There also also more outputs that make our lifes easier:
        
-
          
-
        • support_vectors_ - The array of support vectors
          • 
-
        • n_support_ - The number of support vectors per class
          • 
-
        • dual_coef_ - The coefficients of the support vectors (the dual coefficients)
          • 
-
        
-
        
-
        Exercise 2.1#
        
-
        Evaluate different kernels, with their default hyperparameter settings.
-Outputs should be the 5-fold cross validated accuracy scores for the linear kernel (lin_scores), polynomial kernel (poly_scores) and RBF kernel (rbf_scores). Print the mean and variance of the scores and give an initial interpretation of the performance of each kernel.
        
-
        
-
        Solution#
        
-
        
-
        
-
        #Imports
-from sklearn import svm
-from sklearn.model_selection import cross_val_score
-
-# Linear kernel
-clf = svm.SVC(kernel='linear')
-lin_scores = cross_val_score(clf, X, y)
-
-# Polynomial kernel
-clf = svm.SVC(kernel='poly')
-poly_scores = cross_val_score(clf, X, y)
-
-# RBF kernel
-clf = svm.SVC(kernel='rbf')
-rbf_scores = cross_val_score(clf, X, y)
-
-print("AUC Linear Kernel: {:.2f} +- {:.4f}".format(lin_scores.mean(), np.var(lin_scores)))
-print("AUC Polynomial Kernel: {:.2f} +- {:.4f}".format(poly_scores.mean(), np.var(poly_scores)))
-print("AUC RBF Kernel: {:.2f} +- {:.5f}".format(rbf_scores.mean(), np.var(rbf_scores)))
-
        
-
        
-
        
-
        
-
        AUC Linear Kernel: 0.55 +- 0.0000
-AUC Polynomial Kernel: 0.64 +- 0.0000
-AUC RBF Kernel: 0.90 +- 0.00005
-
        
-
        
-
        
-
        
-
        The linear kernel has a very low score, and is likely underfitting severely.
-The polynomial kernel does a lot better. The RBF kernel works particularly well, even without any tuning.
-The models are very stable, there is hardly any variance in the scores.
        
-
        
-
        
-
        
-
        
-
        Exercise 2: Visualizing the fit#
        
-
        To better understand what the different kernels are doing, let’s visualize their predictions.
        
-
        
-
        Exercise 2.1#
        
-
        Call and fit SVM with linear, polynomial and RBF kernels with default parameter values. For RBF kernel, use kernel coefficient value (gamma) of 2.0. Plot the results for each kernel with “plot_svm_kernel” function. The plots show the predictions made for the different kernels. The background color shows the prediction (blue or red). The full line shows the decision boundary, and the dashed line the margin. The encircled points are the support vectors.
        
-
        
-
        Solution#
        
-
        
-
        
-
        plt.rcParams['figure.dpi'] = 120 # Make figures a bit bigger
-
-#Linear
-clf1 = svm.SVC(kernel='linear', C=1.0, tol=1e-3)  #default values for parameters
-clf1.fit(X, y)
-plot_svm_kernel(X,y,"Linear kernel", 
-                clf1.support_vectors_, 
-                clf1.decision_function, clf1.dual_coef_)
-
-#Polynomial
-clf2 = svm.SVC(kernel='poly', C=1.0)
-clf2.fit(X, y)
-plot_svm_kernel(X,y,"Polynomial kernel", 
-                clf2.support_vectors_, 
-                clf2.decision_function, clf2.dual_coef_)
-
-#RBF
-clf3 = svm.SVC(kernel='rbf', gamma=2, C=1.0)
-clf3.fit(X,y)
-plot_svm_kernel(X,y,"RBF kernel", 
-                clf3.support_vectors_, 
-                clf3.decision_function, clf3.dual_coef_)
-
        
-
        
-
        
-
        
-../_images/41d6bbd6e04a3019614e45f24cd874149b2a7007c4d1e00a66636ff25f500a3a.png
-../_images/5867ed814d5072a5c6d42be594087988e7512bc8da232f0e9f0949198b4d5266.png
-../_images/8e5a6f1eb09ba37c60e6c69363f53f73c891efeaa4b2f4b43605cc086140e6e0.png
-
        
-
        
-
        
-
        
-
        
-
        Exercise 2.2#
        
-
        Interpret the plots for each kernel. Think of ways to improve the results.
        
-
        
-
        Solution#
        
-
        Linear: It’s clear that this data is not linearly separable. The linear SVM is badly underfitting. There also appear to be some optimization issues, as the decision boundary lies way outside of the image, and there is a group of non-support vectors that should be support vectors. Forcing more optimization (by decreasing tolerance of the stopping criterion tol) yields slightly better results, but will also slow down the optimization (try it of you like).
        
-
        Polynomial: A slightly better fit, but clearly polynomials aren’t the best fit either. They divide the space in subspaces that don’t capture the banana shapes at all.
        
-
        RBF: Works very nicely, and the default settings seem to actually hit the sweet spot. We should still try to tune C and gamma.
        
-
        
-
        
-
        
-
        
-
        Exercise 3: Visualizing the RBF models and hyperparameter space#
        
-
        Select the RBF kernel and optimize the two most important hyperparameters (the 𝐶 parameter and the kernel width 𝛾 ).
        
-
        Hint: values for C and \(\gamma\) are typically in [\(2^{-15}..2^{15}\)] on a log scale.
        
-
        
-
        Exercise 3.1#
        
-
        First try 3 very different values for \(C\) and \(\gamma\) (for instance [1e-3,1,1e3]). For each of the 9 combinations, create the same RBF plot as before to understand what the model is doing. Also create a standard train-test split and report the train and test score. Explain the performance results. When are you over/underfitting? Can you see this in the predictions?
        
-
        
-
        Solution#
        
-
        
-
        
-
        from sklearn.model_selection import train_test_split
-
-# For convenience we'll plot the results in a 3x3 grid
-plt.figure(figsize=(15, 10))
-fig_num = 0
-
-# build a standard stratified train-test split
-X_train, X_test, y_train, y_test = train_test_split(X,y, stratify=y, random_state=0)
-
-for c in [0.001, 1, 1000]:
-    for gamma in [0.001, 1, 1000]:
-        fig_num += 1
-        plt.subplot(3, 3, fig_num) # plot in a 3x3 grid
-        clf4 = svm.SVC(kernel='rbf',C=float(c),gamma=float(gamma)) # setup and fit the model
-        clf4.fit(X_train, y_train)
-        plot_svm_kernel(X_train,y_train,"C={}, g={}, trainACC {:.2f}, testACC {:.2f}".format(c,gamma,clf4.score(X_train,y_train), clf4.score(X_test,y_test)), 
-                clf4.support_vectors_, clf4.decision_function, clf4.dual_coef_, show=False)
-        
-plt.show();
-
        
-
        
-
        
-
        
-../_images/75158ca0b5de067bf9f731e23f6b68105d374dd4f0477b1fc88c0a645b56c3f4.png
-
        
-
        
-
          
-
        • For C = 0.001 (top row), the SVM is always underfitting. The boundaries look very different but all are underfitting because they are over-regularized.
          • 
-
        • For gamma = 1000 (narrow Gaussians, right column), almost all datapoints are support vectors, For higher values of C, they are clearly overfitting: the decision boundaries are islands around each point, the model predicts 0 everywhere else.
          • 
-
        • The best results are found for medium C, medium gamma. This also yields the fewest support vectors. The decision boundaries show that it captures the banana shapes well.
          • 
-
        • Large C values (bottom row) tend to cause more overfitting unless gamma is very small. These two types of regularization clearly interact with each other.
          • 
-
        • For gamma=1, you can also see that the margins for C=1000 are much more narrow than those for C=1. Although not visible in the scores, it is clear that the center model (with the larger margins) will generalize better.
          • 
-
        
-
        
-
        
-
        
-
        Exercise 3.2#
        
-
        Optimize the hyperparameters using a grid search, trying every possible combination of C and gamma. Show a heatmap of the results and report the optimal hyperparameter values. Use at least 10 values for \(C\) and \(\gamma\) in [\(2^{-15}..2^{15}\)] on a log scale. Report accuracy under 3-fold CV. We recommend to use sklearn’s GridSearchCV and the heatmap function defined above. Check their documentation.
        
-
        
-
        Solution#
        
-
        
-
        
-
        from sklearn.model_selection import GridSearchCV
-
-# Define and fit a grid search with 3-fold cross validation for SVM - RBF kernel. 
-# Quite a detailed grid search. May take a while.
-svc = svm.SVC(kernel='rbf')
-resolution = 25
-param_grid = {'C': np.logspace(-12,12,resolution,base=2),
-              'gamma': np.logspace(-12,12,resolution,base=2)}
-grid_search = GridSearchCV(svc, param_grid, cv=3, n_jobs=-1, scoring='accuracy');
-grid_search.fit(X, y);
-
        
-
        
-
        
-
        
-
        
-
        
-
        #Plot with heatmap
-results = pd.DataFrame(grid_search.cv_results_)
-scores = np.array(results.mean_test_score).reshape(resolution, resolution)
-plt.rcParams.update({'font.size': 18})
-fig, axes = plt.subplots(1, 1, figsize=(13, 13))
-heatmap(scores, xlabel='gamma', xticklabels=np.around(param_grid['gamma'],4),
-                      ylabel='C', yticklabels=np.around(param_grid['C'],4), cmap="viridis", fmt="%.2f", ax=axes);
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        We can see that there isn’t really an simple optimal peak in the C-gamma space, but rather a ‘ridge’ of optimal performance. For instance, (gamma=0.25, C=4096) has top performance,
-but so does (gamma=2.0, C=0.25).
        
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        Lab 2b: Model selection: dark matter
        
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        Lab 2b: Model selection: dark matter#
        
-
        We’ll use the MAGIC telescope dataset (http://www.openml.org/d/1120). The task is to classifying gamma rays, which consist of high-energy particles. When they hit our atmosphere, they produce chain reactions of other particles called ‘showers’. However, similar showers are also produced by other particles (hadrons). We want to be able to detect which ones originate from gamma rays and which ones come from background radiation. To do this, the observed shower patterns are observed and converted into 10 numeric features. You need to detect whether these are gamma rays or background radiation. This is a key aspect of research into dark matter, which is believed to generate such gamma rays. If we can detect where they occur, we can build a map of the origins of gamma radiation, and locate where dark matter may occur in the observed universe. However, we’ll first need to accurately detect these gamma rays first.
        
-
        A quick visualization of the features is shown below. Note that this is not a time series, we just plot the instances in the order they occur in the dataset. The first 12500 or so are examples of signal (gamma), the final 6700 or so are background (hadrons).
        
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        # General imports
-%matplotlib inline
-from preamble import *
-plt.rcParams['figure.dpi'] = 100
-
        
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-
        # Download MAGIC Telescope data from OpenML. You can repeat this analysis with any other OpenML classification dataset.
-magic = oml.datasets.get_dataset(1120)
-X, y, _, _ = magic.get_data(target=magic.default_target_attribute, dataset_format='array'); 
-attribute_names = [f.name for i,f in magic.features.items()][:-1][1:]
-
        
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-
        # Quick visualization of the features (top) and the target (bottom)
-magic_df = pd.DataFrame(X, columns=attribute_names)
-magic_df.plot(figsize=(12,6))
-# Also plot the target: 1 = background, 0 = gamma
-pd.DataFrame(y).plot(figsize=(12,1));
-
        
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-../_images/aea41e3795dfde0202769680c3cabdffa37e3e235090bc91b1b10532ae6fb365.png
-../_images/6edb23999cbfb410b472df340710d46407f4309709d9ec9d7843491691b5c6fa.png
-
        
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        Exercise 1: Metrics#
        
-
        Train and evaluate an SVM with RBF kernel (default hyperparameters) using a standard 25% holdout. Report the accuracy, precision, recall, F1 score, and area under the ROC curve (AUC).
        
-
        Answer the following questions:
        
-
          
-
        • How many of the detected gamma rays are actually real gamma rays?
          • 
-
        • How many of all the gamma rays are we detecting?
          • 
-
        • How many false positives and false negatives occur?
          • 
-
        
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        from sklearn.model_selection import train_test_split
-from sklearn.metrics import accuracy_score, f1_score, precision_score, recall_score, roc_auc_score
-from sklearn.svm import SVC
-
-# Default train-test split
-# This is classification, so we definitely want to use stratification again.
-X_train, X_test, y_train, y_test = train_test_split(
-    X, y, stratify=y, random_state=0)
-
-# Train the SVM and retrieve the predictions
-svm = SVC().fit(X_train, y_train)
-y_pred = svm.predict(X_test)
-
        
-
        
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-
        
-
        
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        # Get the scores by comparing the predictions y_pred with the ground truth y_test
-print("Accuracy: {:.3f}".format(accuracy_score(y_test, y_pred)))
-print("Precision: {:.3f}".format(precision_score(y_test, y_pred)))
-print("Recall: {:.3f}".format(recall_score(y_test, y_pred)))
-print("F1 score: {:.3f}".format(f1_score(y_test, y_pred)))
-print("AUC: {:.3f}".format(roc_auc_score(y_test, y_pred)))
-
        
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        Accuracy: 0.824
-Precision: 0.878
-Recall: 0.581
-F1 score: 0.700
-AUC: 0.769
-
        
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        How many of the detected gamma rays are actually real gamma rays?
        
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        This is precision. Hence, about 88%.
        
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        How many of all the gamma rays are we detecting?
        
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        This is recall. Hence, about 58%. That doesn’t seem useful at all.
        
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        How many false positives and false negatives occur?
        
-
        
-
        This we can retrieve from the confusion matrix. Remember that in sklearn, the classes are ordered numerically, so the first class is 0 (negative), the second is 1 (positive). That means that the false positives are on row 0, column 1.
        
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-
        
-
        from sklearn.metrics import confusion_matrix
-cm = confusion_matrix(y_test, y_pred)
-print("There are {} false positives and {} false negatives".format(cm[0,1],cm[1,0]))
-
        
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        There are 135 false positives and 700 false negatives
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        Exercise 2: Preprocessing#
        
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        SVMs require scaling to perform well. For now, use the following code to scale the data (we’ll get back to this in the lab about preprocessing and pipelines). Repeat question 2 on the scaled data. Have the results improved?
        
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-
        
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        from sklearn.preprocessing import StandardScaler
-# Important here is to fit the scaler on the training data alone
-# Then, use it to scale both the training set and test set
-# This assumes that you named your training set X_train. Adapt if needed.
-scaler = StandardScaler().fit(X_train)
-Xs_train = scaler.transform(X_train)
-Xs_test = scaler.transform(X_test)
-
        
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        # Train the SVM and retrieve the predictions
-svm = SVC().fit(Xs_train, y_train)
-y_pred = svm.predict(Xs_test)
-
-# Get the scores by comparing the predictions y_pred with the ground truth y_test
-print("Accuracy: {:.3f}".format(accuracy_score(y_test, y_pred)))
-print("Precision: {:.3f}".format(precision_score(y_test, y_pred)))
-print("Recall: {:.3f}".format(recall_score(y_test, y_pred)))
-print("F1 score: {:.3f}".format(f1_score(y_test, y_pred)))
-print("AUC: {:.3f}".format(roc_auc_score(y_test, y_pred)))
-
        
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        Accuracy: 0.872
-Precision: 0.903
-Recall: 0.711
-F1 score: 0.796
-AUC: 0.835
-
        
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        All scores have improved significantly!
        
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-
        Exercise 3: Hyperparameter optimization#
        
-
        Use 50 iterations of random search to tune the \(C\) and \(gamma\) hyperparameters on the scaled training data. Vary both on a log scale (e.g. from 2^-12 to 2^12). Optimize on AUC and use 3 cross-validation (CV) folds for the inner CV to estimate performance. For the outer loop, just use the train-test split you used before (hence, no nested CV). Report the best hyperparameters and the corresponding AUC score. Is it better than the default? Finally, use them to evaluate the model on the held-out test set, for all 5 metrics we used before.
        
-
        Extra challenge: plot the samples used by the random search (\(C\) vs \(gamma\))
        
-
        Note: The reason we don’t use a nested CV just yet is because we would need to rebuild the scaled training and test set multiple times. This is tedious, unless we use pipelines, which we’ll cover in a future lab.
        
-
        Let’s start with the challenge question and plot the set of points selected by randomsearch.
-We use a loguniform distribution, which returns values uniformly on a log scale, between 1e-12 and 1e12. To sample randomly from this distibution, we use the random value sample function rvs().
        
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        # With scipy 1.4, you can use scipy.stats.loguniform instead
-from sklearn.utils.fixes import loguniform
-
-c_samples = loguniform(1e-12, 1e4).rvs(size=100)
-g_samples = loguniform(1e-12, 1e12).rvs(size=100)
-
-fig, ax = plt.subplots()
-ax.scatter(c_samples,g_samples)
-ax.set_xlabel("C")
-ax.set_ylabel("gamma")
-ax.set_xlim(1e-12, 1e4)
-ax.set_ylim(1e-12, 1e12)
-ax.set_xscale('log')
-ax.set_yscale('log')
-
        
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        from sklearn.model_selection import RandomizedSearchCV
-# We use the loguniform distribution
-# You could also use a large fixed grid [1e-12, 1e-11,...]
-# Large C values slow down training, so we'll limit it to 1e4
-param_grid = {'C': loguniform(1e-12, 1e4), 'gamma': loguniform(1e-12, 1e12)}
-
-# Set cv to 3 to do 3-fold CV
-# Set scoring to 'roc_auc' to optimize AUC
-# Set n_iter to 50 to do 50 iterations
-# njobs = -1 allows parallellization
-# Optionally, set a verbosity level to see intermediate output 
-rs = RandomizedSearchCV(SVC(), param_grid, n_iter=50, cv=3, scoring='roc_auc', verbose=2, n_jobs=-1)
-rs.fit(Xs_train, y_train)
-
        
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        Fitting 3 folds for each of 50 candidates, totalling 150 fits
-
        
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        [Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.
-[Parallel(n_jobs=-1)]: Done  33 tasks      | elapsed:   46.0s
-[Parallel(n_jobs=-1)]: Done 150 out of 150 | elapsed:  3.8min finished
-
        
-
        
-
        RandomizedSearchCV(cv=3, estimator=SVC(), n_iter=50, n_jobs=-1,
-                   param_distributions={'C': <scipy.stats._distn_infrastructure.rv_frozen object at 0x7fca10e3ebe0>,
-                                        'gamma': <scipy.stats._distn_infrastructure.rv_frozen object at 0x7fca114786d8>},
-                   scoring='roc_auc', verbose=2)
-
        
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        print("Best score: {:.4f}",rs.best_score_)
-print("Best hyperparameters:", rs.best_params_)
-
        
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-
        Best score: {:.4f} 0.9101131972886245
-Best hyperparameters: {'C': 462.63302228870276, 'gamma': 0.0035856241778658205}
-
        
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-
        
-
        AUC is indeed a lot better than we found before, but note that is the score of the inner CV, not the test set.
        
-
        Out of interest: are these optimal values close to the defaults we used before? The SVC implementation uses a good heuristic for the defaults: 1 / (n_features * X.var())
        
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-
        print("Default gamma: ",svm._gamma)
-print("Default C: ",svm.C)
-
        
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-
        Default gamma:  0.0999999999483963
-Default C:  1.0
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        Our tuned hyperparameters end up with quite different values.
        
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-
        # Get best estimator, train on the full training set, and evaluate on the test set
-best_svm = rs.best_estimator_.fit(Xs_train,y_train)
-y_pred = best_svm.predict(Xs_test)
-
-# Get the scores by comparing the predictions y_pred with the ground truth y_test
-print("Accuracy: {:.3f}".format(accuracy_score(y_test, y_pred)))
-print("Precision: {:.3f}".format(precision_score(y_test, y_pred)))
-print("Recall: {:.3f}".format(recall_score(y_test, y_pred)))
-print("F1 score: {:.3f}".format(f1_score(y_test, y_pred)))
-print("AUC: {:.3f}".format(roc_auc_score(y_test, y_pred)))
-
        
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        Accuracy: 0.868
-Precision: 0.903
-Recall: 0.700
-F1 score: 0.789
-AUC: 0.830
-
        
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-
        The scores on the test set are slightly lower than we observed before. This likely means that we are overfitting the hyperparameters on the single train test split. Do keep in mind that the result on a single held out test set should be treated with care. It would be best to also do an outer CV to get a better estimate.
        
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-
        
-
        Exercise 4: Threshold calibration#
        
-
        First, plot the Precision-Recall curve for the SVM using the default parameters on the scaled data. Then, calibrate the threshold to find a solution that yields better recall without sacrificing too much precision.
        
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-
        
-
        from sklearn.metrics import precision_recall_curve
-
-# Train model
-model = SVC().fit(Xs_train,y_train)
-
-# SVC is not probabilistic, so we use the decision function to get the ROC curve
-precision, recall, thresholds = precision_recall_curve(y_test, model.decision_function(Xs_test))
-# Find threshold closest to 0
-close_zero = np.argmin(np.abs(thresholds))
-plt.plot(recall[close_zero], precision[close_zero], 'o', markersize=10, label="threshold zero", fillstyle="none", c='k', mew=2)
-
-threshold = -0.28
-close_t = np.argmin(np.abs(thresholds-threshold))
-plt.plot(recall[close_t], precision[close_t], '^', markersize=10, label="better threshold", fillstyle="none", c='r', mew=2)
-
-threshold = -1.175
-close_t = np.argmin(np.abs(thresholds-threshold))
-plt.plot(recall[close_t], precision[close_t], 's', markersize=10, label="threshold -1.175", fillstyle="none", c='r', mew=2)
-
-plt.plot(recall, precision, lw=2, label="ROC curve")
-plt.ylabel("Precision")
-plt.xlabel("Recall")
-plt.legend(loc="best");
-
        
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-../_images/799246109b97f6bb845f2bf048384e8edd8e78be7e52556398ceb9cc184e8845.png
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        The Precision-recall curve is really smooth. Every improvement in recall will equally reduce precision. We can move a little bit to the right. There is a small drop around threshold -0.28. That means we will be predicting more points as positive.
        
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-
        
-
        Exercise 5: Cost function#
        
-
        Assume that a false negative is twice as bad (costly) than a false positive. I.e. we would rather waste time checking gamma ray sources that are not real, than missing an interesting gamma ray source. Use ROC analysis to find the optimal threshold under this assumption.
        
-
        Finally, let the model make predictions using the optimal threshold and report all 5 scores. Is recall better now? Did we lose a lot of precision?
        
-
        
-
        
-
        from sklearn.metrics import roc_curve
-
-# Reusing code for the lecture notebook
-# Cost function, give the cost for FN and FP
-def cost(fpr, tpr, cost_FN, cost_FP, ratio_P):
-    return fpr * cost_FP * ratio_P + (1 - tpr) * (1 - ratio_P) * cost_FN;
-
-def plot_isometrics(c_FN=2, c_FP=1):
-    # Build the ROC curve for the trained model
-    fpr, tpr, thresholds = roc_curve(y_test, model.decision_function(Xs_test))
-
-    # Compute costs
-    ratio_P = len(y_test[y_test==1]) / len(y_test)
-    costs = [cost(fpr[x],tpr[x],c_FN,c_FP, ratio_P) for x in range(len(thresholds))]
-    
-    # Get optimal cost and threshold
-    min_cost = np.min(costs)
-    min_thres = np.argmin(costs)
-    min_thres_val = thresholds[np.argmin(costs)]
-
-    # plot contours
-    x = np.arange(0.0, 1.1, 0.1)
-    y = np.arange(0.0, 1.1, 0.1)
-    XX, YY = np.meshgrid(x, y)
-    costs = [cost(f, t, c_FN, c_FP, ratio_P) for f, t in zip(XX,YY)]
-
-    # plot all together
-    fig, axes = plt.subplots(1, 1, figsize=(9, 3))
-    plt.plot(fpr, tpr, label="ROC Curve")
-    levels = np.linspace(np.array(costs).min(), np.array(costs).max(), 10)
-    levels = np.sort(np.append(levels, min_cost))
-    CS = plt.contour(XX, YY, costs, levels)
-    plt.clabel(CS, inline=1, fontsize=10)
-
-    plt.xlabel("FPR")
-    plt.ylabel("TPR (recall)")
-    # find threshold closest to zero:
-    plt.plot(fpr[min_thres], tpr[min_thres], 'o', markersize=4,
-             label="optimal: {:.4f}".format(min_thres_val), fillstyle="none", c='k', mew=2)
-    plt.legend(loc=4);
-    plt.title("Isometrics, cost_FN: {}, cost_FP: {}".format(c_FN, c_FP))
-    plt.show()
-    
-plot_isometrics()
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-../_images/69f4ce656fa150ede224a3ff8237fc014598d21bb79953a7157728bc0e59c9ea.png
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        Under this cost function, the ideal threshold is -1.175.
-Now, let’s evaluate what this means for the model’s performance.
        
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        y_pred = (model.decision_function(Xs_test) >= -1.175).astype(int)
-
-# Get the scores by comparing the predictions y_pred with the ground truth y_test
-print("Accuracy: {:.3f}".format(accuracy_score(y_test, y_pred)))
-print("Precision: {:.3f}".format(precision_score(y_test, y_pred)))
-print("Recall: {:.3f}".format(recall_score(y_test, y_pred)))
-print("F1 score: {:.3f}".format(f1_score(y_test, y_pred)))
-print("AUC: {:.3f}".format(roc_auc_score(y_test, y_pred)))
-
        
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        Accuracy: 0.748
-Precision: 0.591
-Recall: 0.926
-F1 score: 0.721
-AUC: 0.789
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        The recall score improved massively (from 71% to 93%), but we also lost a lot of precision (from 90% to 59%). If we plot this threshold in the precision-recall curve (see previous question), we see that it is indeed giving high recall but low precision. Accuracy and AUC also reduced quite a bit. However, if recall is what we really care about, this would still be a good solution.
        
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-      © Copyright 2023. CC0 Licensed - Use as you like. Appropriate credit is very welcome.
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        Lab 4: Using trees to detect trees
        
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        Lab 4: Using trees to detect trees#
        
-
        We will be using tree-based ensemble methods on the Covertype dataset.
-It contains about 100,000 observations of 7 types of trees (Spruce, Pine, Cottonwood, Aspen,…) described by 55 features describing elevation, distance to water, soil type, etc.
        
-
        
-
        
-
        %matplotlib inline
-# imports
-import pandas as pd
-import numpy as np
-import matplotlib.pyplot as plt
-import openml
-import time
-from tqdm import tqdm, tqdm_notebook
-import seaborn as sns # Plotting library, install with 'pip install seaborn'
-
        
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-
        
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        # Download Covertype data. Takes a while the first time.
-covertype = openml.datasets.get_dataset(180)
-X, y, _, _ = covertype.get_data(target=covertype.default_target_attribute, dataset_format='array'); 
-classes = covertype.retrieve_class_labels()
-features = [f.name for i,f in covertype.features.items()][:-1]
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        classes
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        ['Spruce_Fir',
- 'Lodgepole_Pine',
- 'Ponderosa_Pine',
- 'Cottonwood_Willow',
- 'Aspen',
- 'Douglas_fir',
- 'Krummholz']
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        features[0:20]
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        ['elevation',
- 'aspect',
- 'slope',
- 'horizontal_distance_to_hydrology',
- 'Vertical_Distance_To_Hydrology',
- 'Horizontal_Distance_To_Roadways',
- 'Hillshade_9am',
- 'Hillshade_Noon',
- 'Hillshade_3pm',
- 'Horizontal_Distance_To_Fire_Points',
- 'wilderness_area1',
- 'wilderness_area2',
- 'wilderness_area3',
- 'wilderness_area4',
- 'soil_type_1',
- 'soil_type_2',
- 'soil_type_3',
- 'soil_type_4',
- 'soil_type_5',
- 'soil_type_6']
-
        
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        To understand the data a bit better, we can use a scatter matrix. From this, it looks like elevation is a relevant feature.
-Douglas Fir and Aspen grow at low elevations, while only Krummholz pines survive at very high elevations.
        
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-
        # Using seaborn to build the scatter matrix
-# only first 3 columns, first 1000 examples
-n_points = 1500
-df = pd.DataFrame(X[:n_points,:3], columns=features[:3])
-df['class'] = [classes[i] for i in y[:n_points]]
-sns.set(style="ticks")
-sns.pairplot(df, hue="class");
-
        
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-../_images/546c29969c9c12df0a26adf9b9aab6ab950b9dc0a64b99be72f48804bf2fb762.png
-
        
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-
        Exercise 1: Random Forests#
        
-
        Implement a function evaluate_RF that measures the performance of a Random Forest Classifier, using trees
-of (max) depth 2,8,32,64, for any number of trees in the ensemble (n_estimators).
-For the evaluation you should measure accuracy using 3-fold cross-validation.
-Use random_state=1 to ensure reproducibility. Finally, plot the results for at least 5 values of n_estimators ranging from 1 to 30. You can, of course, reuse code from earlier labs and assignments. Interpret the results.
-You can take a 50% subsample to speed the plotting.
        
-
        
-
        
-
        ## Model solution
-from IPython import display
-def plot_live(X, y, evaluator, param_name, param_range, scale='log', ylim=(0,1), ylabel='score', marker = '.'):
-    """ Renders a plot that updates with every evaluation from evaluator.
-    Keyword arguments:
-    X -- the data for training and testing
-    y -- the correct labels
-    evaluator -- a function with signature (X, y, param_value) that returns a dictionary of scores.
-                 Examples: {"train": 0.9, "test": 0.95} or {"model_1": 0.9, "model_2": 0.7}
-    param_name -- the parameter that is being varied on the X axis. Can be a hyperparameter, sample size,...
-    param_range -- list of all possible values on the x-axis
-    scale -- defines which scale to plot the x-axis on, either 'log' (logarithmic) or 'linear'
-    ylim -- tuple with the lowest and highest y-value to plot (e.g. (0, 10))
-    ylabel -- the y-axis title
-    """
-    # Plot interactively
-    plt.ion()
-    plt.ylabel(ylabel)
-    plt.xlabel(param_name)
-    
-    # Make the scale look nice
-    plt.xscale(scale)
-    plt.xlim(param_range[0],param_range[-1])
-    plt.ylim(ylim)
-        
-    # Start from empty plot, then fill it
-    series = {}
-    lines = {}
-    xvals = []
-    for i in param_range:
-        scores = evaluator(X, y, i) 
-        if i == param_range[0]: # initialize series
-            for k in scores.keys():
-                lines[k], = plt.plot(xvals, [], marker = marker, label = k)
-                series[k] = []
-        xvals.append(i)
-        for k in scores.keys(): # append new data
-            series[k].append(scores[k])
-            lines[k].set_data(xvals, series[k])
-        # refresh plot
-        plt.legend(loc='best')
-        plt.margins(0.1)
-        display.display(plt.gcf())
-        display.clear_output(wait=True)
-
        
-
        
-
        
-
        
-
        
-
        
-
        ## Model solution
-from sklearn.ensemble import RandomForestClassifier, GradientBoostingClassifier
-from sklearn.model_selection import cross_val_score, train_test_split
-from sklearn.metrics import balanced_accuracy_score
-from xgboost import XGBClassifier
-
-def evaluate_RF(X, y, n_estimators, max_depth=[2,8,32,64], scoring='accuracy'):
-    """ Evaluate a Random Forest classifier using 3-fold cross-validation on the provided (X, y) data. 
-    Keyword arguments:
-    X -- the data for training and testing
-    y -- the correct labels
-    n_estimators -- the value for the gamma parameter
-    
-    Returns: a dictionary with the train and test score, e.g. {"rf_1": 0.9, "rf_2": 0.95}
-    """
-    res = {}
-    for md in max_depth:
-        rf = RandomForestClassifier(n_estimators=n_estimators, max_depth=md, random_state=1)
-        res['rf_'+str(md)] = np.mean(cross_val_score(rf,X,y,cv=3,scoring=scoring))
-    return res
-
        
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-
        def plot_1(X, y, evaluator):
-    Xs, _, ys, _ = train_test_split(X,y, stratify=y, train_size=0.5, random_state=1)
-    param_name = 'n_estimators'
-    param_range = range(1, 32, 5)
-    plot_live(Xs, ys, evaluator, param_name, param_range, scale='linear')
-plot_1(X, y, evaluate_RF)
-
        
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-../_images/7b112a321628fc9eb220c22164152626a8828ab76dae7050c883703ade203b84.png
-
        
-
        
-
        Overall, the more trees, the better the score. The depth of the tree has a much larger
-effect though. Trees smaller than 32 do not perform well in the ensemble.
-This is to be expected, since Random Forests is a variance-reduction technique. It will
-only work if the trees are allowed to overfit. If they underfit, building a random forest
-ensemble of them won’t help. However, trees deeper than 32 do not further improve the score, likely because the trees don’t grow much deeper on this dataset.
        
-
        
-
        
-
        Exercise 2: Other measures#
        
-
        Repeat the same plot but now use balanced_accuracy as the evaluation measure. See the documentation.
-Only use the optimal max_depth from the previous question. Do you see an important difference?
        
-
        
-
        
-
        ## Model solution
-def evaluate_RF_balanced(X,y,n_estimators):
-    return evaluate_RF(X,y,n_estimators,max_depth=[32], scoring='balanced_accuracy')
-plot_1(X, y, evaluate_RF_balanced)
-
        
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-../_images/dc75447dafd3a307546b1964401b62e06fd4774ac20e22bf196476bbb91423bd.png
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-
        Exercise 3: Feature importance#
        
-
        Retrieve the feature importances according to the (tuned) random forest model. Which feature are most important?
        
-
        
-
        
-
        ## Model solution
-def plot_feature_importances(features, model):
-    n_features = len(features)
-    plt.figure(figsize=(5,10))
-    plt.barh(range(n_features), model.feature_importances_, align='center')
-    plt.yticks(range(n_features), features)
-    plt.xlabel("Feature importance")
-    plt.ylabel("Feature")
-    plt.ylim(-1, n_features)
-
-forest = RandomForestClassifier(random_state=0, n_estimators=25, max_depth=32, n_jobs=-1)
-forest.fit(X,y)
-plt.rcParams.update({'font.size':8})
-plot_feature_importances(features, forest)
-
        
-
        
-
        
-
        
-../_images/9bba206ebe8896eb66c9d8d8d51a468488cee0948bc61aaef81cd25d7ef86e1a.png
-
        
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-
        
-
        
-
        Exercise 4: Feature selection#
        
-
        Re-build your tuned random forest, but this time only using the first 10 features.
-Return both the balanced accuracy and training time. Interpret the results.
        
-
        
-
        
-
        # Model Solution
-start = time.time()
-score = evaluate_RF(X,y,25,max_depth=[32], scoring='balanced_accuracy')
-print("Normal RF: {:.2f} balanced ACC, {:.2f} seconds".format(score['rf_32'], (time.time()-start)))
-start = time.time()
-score = evaluate_RF(X[:,0:10],y,25,max_depth=[32], scoring='balanced_accuracy')
-print("Feature Selection RF: {:.2f} balanced ACC, {:.2f} seconds".format(score['rf_32'], (time.time()-start)))
-
        
-
        
-
        
-
        
-
        Normal RF: 0.65 balanced ACC, 15.26 seconds
-Feature Selection RF: 0.62 balanced ACC, 16.49 seconds
-
        
-
        
-
        
-
        
-
        The first 10 features are the most significant according to the random forest. If we select only those, we get a very similar (but slightly worse) result. Random forests is already very robust against irrelevant features. Removing irrelevant features
-in this way doesn’t help much. The runtime is also about the same.
        
-
        
-
        
-
        Exercise 5: Confusion matrix#
        
-
        Do a standard stratified holdout and generate the confusion matrix of the tuned random forest. Which classes are still often confused?
        
-
        
-
        
-
        # Model Solution
-X_train, X_test, y_train, y_test = train_test_split(X,y, stratify=y, random_state=1)
-tuned_forest = RandomForestClassifier(random_state=0, n_estimators=25, max_depth=32, n_jobs=-1).fit(X_train, y_train)
-
        
-
        
-
        
-
        
-
        
-
        
-
        # Model Solution
-from sklearn.metrics import confusion_matrix
-confusion_matrix(y_test, tuned_forest.predict(X_test))
-
        
-
        
-
        
-
        
-
        array([[ 8475,  1059,    41,    20,    30,    23,    79],
-       [  661, 12032,    73,    22,    35,    67,    31],
-       [   83,   167,  1510,     8,    10,    55,    11],
-       [   81,   114,    39,    81,     4,    12,     4],
-       [  103,   250,    19,     3,   260,    11,     7],
-       [   89,   173,   113,     5,     2,   600,    10],
-       [  173,   121,    14,     2,    10,     8,   799]])
-
        
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-
        Exercise 6: A second-level model#
        
-
        Build a binary model specifically to correctly choose between the first and the second class.
-Select only the data points with those classes and train a new random forest. Do a standard stratified split and plot the resulting ROC curve. Can we still improve the model by calibrating the threshold?
        
-
        
-
        
-
        # Model Solution
-X_bin = X[y < 2, :]
-y_bin = y[y < 2]
-
        
-
        
-
        
-
        
-
        
-
        
-
        # Model Solution
-def plot_1(X, y, evaluator):
-    param_name = 'n_estimators'
-    param_range = range(1, 32, 5)
-    plot_live(X, y, evaluator, param_name, param_range, scale='linear')
-plot_1(X_bin, y_bin, evaluate_RF)
-
        
-
        
-
        
-
        
-../_images/02d8724a5fb4799c8660a6e0a0ad923ac66cc60302c5e9d0c1645f3268a19f54.png
-
        
-
        
-
        The previously tuned hyperparameters are still good.
        
-
        
-
        
-
        # Model Solution
-from sklearn.metrics import roc_curve
-
-X_train, X_test, y_train, y_test = train_test_split(X_bin,y_bin, stratify=y_bin, random_state=1)
-binary_forest = RandomForestClassifier(random_state=0, n_estimators=25, max_depth=32, n_jobs=-1).fit(X_train, y_train)
-fpr_rf, tpr_rf, thresholds_rf = roc_curve(y_test, binary_forest.predict_proba(X_test)[:, 1])
-
-plt.plot(fpr_rf, tpr_rf, label="ROC Curve RF")
-plt.xlabel("FPR")
-plt.ylabel("TPR (recall)")
-close_default_rf = np.argmin(np.abs(thresholds_rf - 0.5))
-plt.plot(fpr_rf[close_default_rf], tpr_rf[close_default_rf], '^', markersize=10,
-         label="threshold 0.5 RF", fillstyle="none", c='k', mew=2)
-plt.legend(loc=4);
-
        
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-../_images/4fa40a9d08879de74e9cc12ab9ebf1ddfae8996bff6b39dac00012fde4e9a988.png
-
        
-
        
-
        Yes, we want to be in the top left corner. Setting the threshold at 0.6 seems te be better.
        
-
        
-
        
-
        # Model Solution
-# Too much code replication
-plt.plot(fpr_rf, tpr_rf, label="ROC Curve RF")
-plt.xlabel("FPR")
-plt.ylabel("TPR (recall)")
-close_default_rf = np.argmin(np.abs(thresholds_rf - 0.6))
-plt.plot(fpr_rf[close_default_rf], tpr_rf[close_default_rf], '^', markersize=10,
-         label="threshold 0.5 RF", fillstyle="none", c='k', mew=2)
-plt.legend(loc=4);
-
        
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-../_images/492ca4fe7cb32ae676dd463613fb4ee90120dbaf8915c175f9e85ca683b8a00f.png
-
        
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-
        Exercise 7: Model calibration#
        
-
        For the trained binary random forest model, plot a calibration curve (see course notebook).
-Next, try to correct for this using Platt Scaling (or sigmoid scaling).
        
-
        Probability calibration should be done on new data not used for model fitting. The class CalibratedClassifierCV uses a cross-validation generator and estimates for each split the model parameter on the train samples and the calibration of the test samples. The probabilities predicted for the folds are then averaged. Already fitted classifiers can be calibrated by CalibratedClassifierCV via the parameter cv=”prefit”. Read more
        
-
        
-
        
-
        # Model Solution
-from sklearn.calibration import calibration_curve
-def plot_calibration_curve(y_true, y_prob, n_bins=5, ax=None, hist=True, normalize=False):
-    prob_true, prob_pred = calibration_curve(y_true, y_prob, n_bins=n_bins, normalize=normalize)
-    if ax is None:
-        ax = plt.gca()
-    if hist:
-        ax.hist(y_prob, weights=np.ones_like(y_prob) / len(y_prob), alpha=.4,
-               bins=np.maximum(10, n_bins))
-    ax.plot([0, 1], [0, 1], ':', c='k')
-    curve = ax.plot(prob_pred, prob_true, marker="o")
-
-    ax.set_xlabel("predicted probability")
-    ax.set_ylabel("fraction of positive samples")
-
-    ax.set(aspect='equal')
-    return curve
-
-X_train, X_test, y_train, y_test = train_test_split(X_bin,y_bin, stratify=y_bin, random_state=1)
-binary_forest = RandomForestClassifier(random_state=0, n_estimators=25, max_depth=32, n_jobs=-1).fit(X_train, y_train)
-scores = forest.predict_proba(X_test)[:, 1]
-plot_calibration_curve(y_test, scores, n_bins=20);
-
        
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-../_images/1392fda1c03380b68b68c944f673558226750f331091d15dd1860c9b3b868477.png
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-
        # Model Solution
-from sklearn.calibration import CalibratedClassifierCV
-rf = RandomForestClassifier(random_state=0, n_estimators=25, max_depth=32, n_jobs=-1) #Unfitted RF
-sigmoid = CalibratedClassifierCV(rf, cv=2, method='sigmoid')
-sigmoid.fit(X_train, y_train)
-y_pred = sigmoid.predict(X_test)
-prob_pos = sigmoid.predict_proba(X_test)[:, 1]
-plot_calibration_curve(y_test, prob_pos, n_bins=20);
-
        
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-
        Exercise 8: Gradient Boosting#
        
-
        Implement a function evaluate_GB that measures the performance of GradientBoostingClassifier or the XGBoostClassifier for
-different learning rates (0.01, 0.1, 1, and 10). As before, use a 3-fold cross-validation. You can use a 5% stratified sample of the whole dataset.
-Finally plot the results for n_estimators ranging from 1 to 100. Run all the GBClassifiers with random_state=1 to ensure reproducibility.
        
-
        Implement a function that plots the score of evaluate_GB for n_estimators = 10,20,30,…,100 on a linear scale.
        
-
        
-
        
-
        # Model Solution
-# This could be done more efficiently using warm starting
-
-from sklearn.ensemble import GradientBoostingClassifier
-from sklearn.model_selection import train_test_split, StratifiedKFold
-from xgboost import XGBClassifier
-
-def evaluate_GB(X, y, n_estimators, learning_rate=[0.01,0.1,1,10], scoring='accuracy'):
-    res = {}
-    for lr in learning_rate:
-        rf = GradientBoostingClassifier(n_estimators=n_estimators, learning_rate=lr, random_state=1)
-        kfold = StratifiedKFold(n_splits=3, random_state=1, shuffle=True)
-        res['gb_'+str(lr)] = np.mean(cross_val_score(rf,X,y,cv=kfold,scoring=scoring))
-    return res
-
-def plot_2(X, y, evaluator):
-    Xs, _, ys, _ = train_test_split(X,y, stratify=y, train_size=0.05, random_state=1)
-    param_name = 'n_estimators'
-    param_range = range(1, 150, 20)
-    plot_live(Xs, ys, evaluator, param_name, param_range, scale='linear')
-plot_2(X, y, evaluate_GB)
-
        
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-../_images/94903771467885d601f263c974ce7ea6735393ff6a5c57113769516c089238f5.png
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-
        We notice that gradient boosting is a lot slower to train that random forests, and it performs less well (at least when using fewer than 150 iterations).
-A smaller learning rate requires more iterations but ultimately works out best. It is possible that the model with learning rate 0.01 will ultimately overtake the one with learning rate 0.1 but it may also take a long time.
        
-
        A learning rate that is too large performs poorly. For learning_rate=1, the model starts out well, but gradually performs worse. The instance weights are adapted so aggressively that the next model does not actually fix the mistakes of the previous model but ‘overshoots’ and introduces more errors in the ensemble. After a while, it is not capable to make fine enough adjustments and levels off, not improving the model anymore. A more detailed explanation can be read here.
        
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-    Lab 4: Using trees to detect trees — ML Engineering
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-         Contents
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        Lab 4: Using trees to detect trees
        
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        Lab 4: Using trees to detect trees#
        
-
        We will be using tree-based ensemble methods on the Covertype dataset.
-It contains about 100,000 observations of 7 types of trees (Spruce, Pine, Cottonwood, Aspen,…) described by 55 features describing elevation, distance to water, soil type, etc.
        
-
        
-
        
-
        %matplotlib inline
-# imports
-import pandas as pd
-import numpy as np
-import matplotlib.pyplot as plt
-import openml
-import time
-from tqdm import tqdm, tqdm_notebook
-import seaborn as sns # Plotting library, install with 'pip install seaborn'
-
        
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-
        
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-
        
-
        # Download Covertype data. Takes a while the first time.
-covertype = openml.datasets.get_dataset(180)
-X, y, _, _ = covertype.get_data(target=covertype.default_target_attribute, dataset_format='array'); 
-classes = covertype.retrieve_class_labels()
-features = [f.name for i,f in covertype.features.items()][:-1]
-
        
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        classes
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        ['Spruce_Fir',
- 'Lodgepole_Pine',
- 'Ponderosa_Pine',
- 'Cottonwood_Willow',
- 'Aspen',
- 'Douglas_fir',
- 'Krummholz']
-
        
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        features[0:20]
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        ['elevation',
- 'aspect',
- 'slope',
- 'horizontal_distance_to_hydrology',
- 'Vertical_Distance_To_Hydrology',
- 'Horizontal_Distance_To_Roadways',
- 'Hillshade_9am',
- 'Hillshade_Noon',
- 'Hillshade_3pm',
- 'Horizontal_Distance_To_Fire_Points',
- 'wilderness_area1',
- 'wilderness_area2',
- 'wilderness_area3',
- 'wilderness_area4',
- 'soil_type_1',
- 'soil_type_2',
- 'soil_type_3',
- 'soil_type_4',
- 'soil_type_5',
- 'soil_type_6']
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-
        To understand the data a bit better, we can use a scatter matrix. From this, it looks like elevation is a relevant feature.
-Douglas Fir and Aspen grow at low elevations, while only Krummholz pines survive at very high elevations.
        
-
        
-
        
-
        # Using seaborn to build the scatter matrix
-# only first 3 columns, first 1000 examples
-n_points = 1500
-df = pd.DataFrame(X[:n_points,:3], columns=features[:3])
-df['class'] = [classes[i] for i in y[:n_points]]
-sns.set(style="ticks")
-sns.pairplot(df, hue="class");
-
        
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-../_images/Lab 3b - Ensembles Solution_6_0.png
-
        
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-
        
-
        Exercise 1: Random Forests#
        
-
        Implement a function evaluate_RF that measures the performance of a Random Forest Classifier, using trees
-of (max) depth 2,8,32,64, for any number of trees in the ensemble (n_estimators).
-For the evaluation you should measure accuracy using 3-fold cross-validation.
-Use random_state=1 to ensure reproducibility. Finally, plot the results for at least 5 values of n_estimators ranging from 1 to 30. You can, of course, reuse code from earlier labs and assignments. Interpret the results.
-You can take a 50% subsample to speed the plotting.
        
-
        
-
        
-
        ## Model solution
-from IPython import display
-def plot_live(X, y, evaluator, param_name, param_range, scale='log', ylim=(0,1), ylabel='score', marker = '.'):
-    """ Renders a plot that updates with every evaluation from evaluator.
-    Keyword arguments:
-    X -- the data for training and testing
-    y -- the correct labels
-    evaluator -- a function with signature (X, y, param_value) that returns a dictionary of scores.
-                 Examples: {"train": 0.9, "test": 0.95} or {"model_1": 0.9, "model_2": 0.7}
-    param_name -- the parameter that is being varied on the X axis. Can be a hyperparameter, sample size,...
-    param_range -- list of all possible values on the x-axis
-    scale -- defines which scale to plot the x-axis on, either 'log' (logarithmic) or 'linear'
-    ylim -- tuple with the lowest and highest y-value to plot (e.g. (0, 10))
-    ylabel -- the y-axis title
-    """
-    # Plot interactively
-    plt.ion()
-    plt.ylabel(ylabel)
-    plt.xlabel(param_name)
-    
-    # Make the scale look nice
-    plt.xscale(scale)
-    plt.xlim(param_range[0],param_range[-1])
-    plt.ylim(ylim)
-        
-    # Start from empty plot, then fill it
-    series = {}
-    lines = {}
-    xvals = []
-    for i in param_range:
-        scores = evaluator(X, y, i) 
-        if i == param_range[0]: # initialize series
-            for k in scores.keys():
-                lines[k], = plt.plot(xvals, [], marker = marker, label = k)
-                series[k] = []
-        xvals.append(i)
-        for k in scores.keys(): # append new data
-            series[k].append(scores[k])
-            lines[k].set_data(xvals, series[k])
-        # refresh plot
-        plt.legend(loc='best')
-        plt.margins(0.1)
-        display.display(plt.gcf())
-        display.clear_output(wait=True)
-
        
-
        
-
        
-
        
-
        
-
        
-
        ## Model solution
-from sklearn.ensemble import RandomForestClassifier, GradientBoostingClassifier
-from sklearn.model_selection import cross_val_score, train_test_split
-from sklearn.metrics import balanced_accuracy_score
-from xgboost import XGBClassifier
-
-def evaluate_RF(X, y, n_estimators, max_depth=[2,8,32,64], scoring='accuracy'):
-    """ Evaluate a Random Forest classifier using 3-fold cross-validation on the provided (X, y) data. 
-    Keyword arguments:
-    X -- the data for training and testing
-    y -- the correct labels
-    n_estimators -- the value for the gamma parameter
-    
-    Returns: a dictionary with the train and test score, e.g. {"rf_1": 0.9, "rf_2": 0.95}
-    """
-    res = {}
-    for md in max_depth:
-        rf = RandomForestClassifier(n_estimators=n_estimators, max_depth=md, random_state=1)
-        res['rf_'+str(md)] = np.mean(cross_val_score(rf,X,y,cv=3,scoring=scoring))
-    return res
-
        
-
        
-
        
-
        
-
        
-
        
-
        def plot_1(X, y, evaluator):
-    Xs, _, ys, _ = train_test_split(X,y, stratify=y, train_size=0.5, random_state=1)
-    param_name = 'n_estimators'
-    param_range = range(1, 32, 5)
-    plot_live(Xs, ys, evaluator, param_name, param_range, scale='linear')
-plot_1(X, y, evaluate_RF)
-
        
-
        
-
        
-
        
-../_images/Lab 3b - Ensembles Solution_10_0.png
-
        
-
        
-
        Overall, the more trees, the better the score. The depth of the tree has a much larger
-effect though. Trees smaller than 32 do not perform well in the ensemble.
-This is to be expected, since Random Forests is a variance-reduction technique. It will
-only work if the trees are allowed to overfit. If they underfit, building a random forest
-ensemble of them won’t help. However, trees deeper than 32 do not further improve the score, likely because the trees don’t grow much deeper on this dataset.
        
-
        
-
        
-
        Exercise 2: Other measures#
        
-
        Repeat the same plot but now use balanced_accuracy as the evaluation measure. See the documentation.
-Only use the optimal max_depth from the previous question. Do you see an important difference?
        
-
        
-
        
-
        ## Model solution
-def evaluate_RF_balanced(X,y,n_estimators):
-    return evaluate_RF(X,y,n_estimators,max_depth=[32], scoring='balanced_accuracy')
-plot_1(X, y, evaluate_RF_balanced)
-
        
-
        
-
        
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-../_images/Lab 3b - Ensembles Solution_13_0.png
-
        
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-
        Exercise 3: Feature importance#
        
-
        Retrieve the feature importances according to the (tuned) random forest model. Which feature are most important?
        
-
        
-
        
-
        ## Model solution
-def plot_feature_importances(features, model):
-    n_features = len(features)
-    plt.figure(figsize=(5,10))
-    plt.barh(range(n_features), model.feature_importances_, align='center')
-    plt.yticks(range(n_features), features)
-    plt.xlabel("Feature importance")
-    plt.ylabel("Feature")
-    plt.ylim(-1, n_features)
-
-forest = RandomForestClassifier(random_state=0, n_estimators=25, max_depth=32, n_jobs=-1)
-forest.fit(X,y)
-plt.rcParams.update({'font.size':8})
-plot_feature_importances(features, forest)
-
        
-
        
-
        
-
        
-../_images/Lab 3b - Ensembles Solution_15_0.png
-
        
-
        
-
        
-
        
-
        Exercise 4: Feature selection#
        
-
        Re-build your tuned random forest, but this time only using the first 10 features.
-Return both the balanced accuracy and training time. Interpret the results.
        
-
        
-
        
-
        # Model Solution
-start = time.time()
-score = evaluate_RF(X,y,25,max_depth=[32], scoring='balanced_accuracy')
-print("Normal RF: {:.2f} balanced ACC, {:.2f} seconds".format(score['rf_32'], (time.time()-start)))
-start = time.time()
-score = evaluate_RF(X[:,0:10],y,25,max_depth=[32], scoring='balanced_accuracy')
-print("Feature Selection RF: {:.2f} balanced ACC, {:.2f} seconds".format(score['rf_32'], (time.time()-start)))
-
        
-
        
-
        
-
        
-
        Normal RF: 0.65 balanced ACC, 15.26 seconds
-Feature Selection RF: 0.62 balanced ACC, 16.49 seconds
-
        
-
        
-
        
-
        
-
        The first 10 features are the most significant according to the random forest. If we select only those, we get a very similar (but slightly worse) result. Random forests is already very robust against irrelevant features. Removing irrelevant features
-in this way doesn’t help much. The runtime is also about the same.
        
-
        
-
        
-
        Exercise 5: Confusion matrix#
        
-
        Do a standard stratified holdout and generate the confusion matrix of the tuned random forest. Which classes are still often confused?
        
-
        
-
        
-
        # Model Solution
-X_train, X_test, y_train, y_test = train_test_split(X,y, stratify=y, random_state=1)
-tuned_forest = RandomForestClassifier(random_state=0, n_estimators=25, max_depth=32, n_jobs=-1).fit(X_train, y_train)
-
        
-
        
-
        
-
        
-
        
-
        
-
        # Model Solution
-from sklearn.metrics import confusion_matrix
-confusion_matrix(y_test, tuned_forest.predict(X_test))
-
        
-
        
-
        
-
        
-
        array([[ 8475,  1059,    41,    20,    30,    23,    79],
-       [  661, 12032,    73,    22,    35,    67,    31],
-       [   83,   167,  1510,     8,    10,    55,    11],
-       [   81,   114,    39,    81,     4,    12,     4],
-       [  103,   250,    19,     3,   260,    11,     7],
-       [   89,   173,   113,     5,     2,   600,    10],
-       [  173,   121,    14,     2,    10,     8,   799]])
-
        
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-
        Exercise 6: A second-level model#
        
-
        Build a binary model specifically to correctly choose between the first and the second class.
-Select only the data points with those classes and train a new random forest. Do a standard stratified split and plot the resulting ROC curve. Can we still improve the model by calibrating the threshold?
        
-
        
-
        
-
        # Model Solution
-X_bin = X[y < 2, :]
-y_bin = y[y < 2]
-
        
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-
        
-
        
-
        
-
        
-
        # Model Solution
-def plot_1(X, y, evaluator):
-    param_name = 'n_estimators'
-    param_range = range(1, 32, 5)
-    plot_live(X, y, evaluator, param_name, param_range, scale='linear')
-plot_1(X_bin, y_bin, evaluate_RF)
-
        
-
        
-
        
-
        
-../_images/Lab 3b - Ensembles Solution_24_0.png
-
        
-
        
-
        The previously tuned hyperparameters are still good.
        
-
        
-
        
-
        # Model Solution
-from sklearn.metrics import roc_curve
-
-X_train, X_test, y_train, y_test = train_test_split(X_bin,y_bin, stratify=y_bin, random_state=1)
-binary_forest = RandomForestClassifier(random_state=0, n_estimators=25, max_depth=32, n_jobs=-1).fit(X_train, y_train)
-fpr_rf, tpr_rf, thresholds_rf = roc_curve(y_test, binary_forest.predict_proba(X_test)[:, 1])
-
-plt.plot(fpr_rf, tpr_rf, label="ROC Curve RF")
-plt.xlabel("FPR")
-plt.ylabel("TPR (recall)")
-close_default_rf = np.argmin(np.abs(thresholds_rf - 0.5))
-plt.plot(fpr_rf[close_default_rf], tpr_rf[close_default_rf], '^', markersize=10,
-         label="threshold 0.5 RF", fillstyle="none", c='k', mew=2)
-plt.legend(loc=4);
-
        
-
        
-
        
-
        
-../_images/Lab 3b - Ensembles Solution_26_0.png
-
        
-
        
-
        Yes, we want to be in the top left corner. Setting the threshold at 0.6 seems te be better.
        
-
        
-
        
-
        # Model Solution
-# Too much code replication
-plt.plot(fpr_rf, tpr_rf, label="ROC Curve RF")
-plt.xlabel("FPR")
-plt.ylabel("TPR (recall)")
-close_default_rf = np.argmin(np.abs(thresholds_rf - 0.6))
-plt.plot(fpr_rf[close_default_rf], tpr_rf[close_default_rf], '^', markersize=10,
-         label="threshold 0.5 RF", fillstyle="none", c='k', mew=2)
-plt.legend(loc=4);
-
        
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-../_images/Lab 3b - Ensembles Solution_28_0.png
-
        
-
        
-
        
-
        
-
        Exercise 7: Model calibration#
        
-
        For the trained binary random forest model, plot a calibration curve (see course notebook).
-Next, try to correct for this using Platt Scaling (or sigmoid scaling).
        
-
        Probability calibration should be done on new data not used for model fitting. The class CalibratedClassifierCV uses a cross-validation generator and estimates for each split the model parameter on the train samples and the calibration of the test samples. The probabilities predicted for the folds are then averaged. Already fitted classifiers can be calibrated by CalibratedClassifierCV via the parameter cv=”prefit”. Read more
        
-
        
-
        
-
        # Model Solution
-from sklearn.calibration import calibration_curve
-def plot_calibration_curve(y_true, y_prob, n_bins=5, ax=None, hist=True, normalize=False):
-    prob_true, prob_pred = calibration_curve(y_true, y_prob, n_bins=n_bins, normalize=normalize)
-    if ax is None:
-        ax = plt.gca()
-    if hist:
-        ax.hist(y_prob, weights=np.ones_like(y_prob) / len(y_prob), alpha=.4,
-               bins=np.maximum(10, n_bins))
-    ax.plot([0, 1], [0, 1], ':', c='k')
-    curve = ax.plot(prob_pred, prob_true, marker="o")
-
-    ax.set_xlabel("predicted probability")
-    ax.set_ylabel("fraction of positive samples")
-
-    ax.set(aspect='equal')
-    return curve
-
-X_train, X_test, y_train, y_test = train_test_split(X_bin,y_bin, stratify=y_bin, random_state=1)
-binary_forest = RandomForestClassifier(random_state=0, n_estimators=25, max_depth=32, n_jobs=-1).fit(X_train, y_train)
-scores = forest.predict_proba(X_test)[:, 1]
-plot_calibration_curve(y_test, scores, n_bins=20);
-
        
-
        
-
        
-
        
-../_images/Lab 3b - Ensembles Solution_30_0.png
-
        
-
        
-
        
-
        
-
        # Model Solution
-from sklearn.calibration import CalibratedClassifierCV
-rf = RandomForestClassifier(random_state=0, n_estimators=25, max_depth=32, n_jobs=-1) #Unfitted RF
-sigmoid = CalibratedClassifierCV(rf, cv=2, method='sigmoid')
-sigmoid.fit(X_train, y_train)
-y_pred = sigmoid.predict(X_test)
-prob_pos = sigmoid.predict_proba(X_test)[:, 1]
-plot_calibration_curve(y_test, prob_pos, n_bins=20);
-
        
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-../_images/Lab 3b - Ensembles Solution_31_0.png
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-
        
-
        Exercise 8: Gradient Boosting#
        
-
        Implement a function evaluate_GB that measures the performance of GradientBoostingClassifier or the XGBoostClassifier for
-different learning rates (0.01, 0.1, 1, and 10). As before, use a 3-fold cross-validation. You can use a 5% stratified sample of the whole dataset.
-Finally plot the results for n_estimators ranging from 1 to 100. Run all the GBClassifiers with random_state=1 to ensure reproducibility.
        
-
        Implement a function that plots the score of evaluate_GB for n_estimators = 10,20,30,…,100 on a linear scale.
        
-
        
-
        
-
        # Model Solution
-# This could be done more efficiently using warm starting
-
-from sklearn.ensemble import GradientBoostingClassifier
-from sklearn.model_selection import train_test_split, StratifiedKFold
-from xgboost import XGBClassifier
-
-def evaluate_GB(X, y, n_estimators, learning_rate=[0.01,0.1,1,10], scoring='accuracy'):
-    res = {}
-    for lr in learning_rate:
-        rf = GradientBoostingClassifier(n_estimators=n_estimators, learning_rate=lr, random_state=1)
-        kfold = StratifiedKFold(n_splits=3, random_state=1, shuffle=True)
-        res['gb_'+str(lr)] = np.mean(cross_val_score(rf,X,y,cv=kfold,scoring=scoring))
-    return res
-
-def plot_2(X, y, evaluator):
-    Xs, _, ys, _ = train_test_split(X,y, stratify=y, train_size=0.05, random_state=1)
-    param_name = 'n_estimators'
-    param_range = range(1, 150, 20)
-    plot_live(Xs, ys, evaluator, param_name, param_range, scale='linear')
-plot_2(X, y, evaluate_GB)
-
        
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-../_images/Lab 3b - Ensembles Solution_34_0.png
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-
        We notice that gradient boosting is a lot slower to train that random forests, and it performs less well (at least when using fewer than 150 iterations).
-A smaller learning rate requires more iterations but ultimately works out best. It is possible that the model with learning rate 0.01 will ultimately overtake the one with learning rate 0.1 but it may also take a long time.
        
-
        A learning rate that is too large performs poorly. For learning_rate=1, the model starts out well, but gradually performs worse. The instance weights are adapted so aggressively that the next model does not actually fix the mistakes of the previous model but ‘overshoots’ and introduces more errors in the ensemble. After a while, it is not capable to make fine enough adjustments and levels off, not improving the model anymore. A more detailed explanation can be read here.
        
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        Lab 4: Data preprocessing and pipelines
        
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        Lab 4: Data preprocessing and pipelines#
        
-
        We explore the performance of several linear regression models on a real-world dataset, i.e. MoneyBall. See the description on OpenML for more information. In short, this dataset captures performance data from baseball players. The regression task is to accurately predict the number of ‘runs’ each player can score, and understanding which are the most important factors.
        
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        # General imports
-%matplotlib inline
-import pandas as pd
-import openml as oml
-
        
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        # Download MoneyBall data from OpenML
-moneyball = oml.datasets.get_dataset(41021)
-# Get the pandas dataframe (default)
-X, y, _, attribute_names = moneyball.get_data(target=moneyball.default_target_attribute)
-
        
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        Exploratory analysis and visualization#
        
-
        First, we visually explore the data by visualizing the value distribution and the interaction between every other feature in a scatter matrix. We use the target feature as the color variable to see which features are correlated with the target.
        
-
        For the plotting to work, however, we need to remove the categorical features (the first 2) and fill in the missing values. Let’s find out which columns have missing values. This matches what we already saw on the OpenML page (https://www.openml.org/d/41021).
        
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        pd.isnull(X).any()
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        Team            False
-League          False
-Year            False
-RA              False
-W               False
-OBP             False
-SLG             False
-BA              False
-Playoffs        False
-RankSeason       True
-RankPlayoffs     True
-G               False
-OOBP             True
-OSLG             True
-dtype: bool
-
        
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        For this first quick visualization, we will simply impute the missing values using the median. Removing all instances with missing values is not really an option since some features have consistent missing values: we would have to remove a lot of data.
        
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-
        
-
        # Impute missing values with sklearn and rebuild the dataframe
-from sklearn.impute import SimpleImputer
-imputer = SimpleImputer(strategy="median")
-X_clean_array = imputer.fit_transform(X[attribute_names[2:]]) # skip the first 2 features
-# The imputer will return a numpy array. To plot it we make it a pandas dataframe again.
-X_clean = pd.DataFrame(X_clean_array, columns = attribute_names[2:]) #
-
        
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        Next, we build the scatter matrix. We include the target column to see which features strongly correlate with the target, and also use the target value as the color to see which combinations of features correlate with the target.
        
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        from pandas.plotting import scatter_matrix
-
-# Scatter matrix of dataframe including the target feature
-copyframe = X_clean.copy() 
-copyframe['y'] = pd.Series(y, index=copyframe.index)
-scatter_matrix(copyframe, c=y, figsize=(25,25), 
-               marker='o', s=20, alpha=.8, cmap='viridis');
-
        
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-../_images/4d4de1353ded20f6ae577478ff3f15706819ad0e78bde5de7bc9398e3d47efad.png
-
        
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-
        Several things immediately stand out:
        
-
          
-
        • OBP, SLG and BA strongly correlate with the target (near-diagonals in the final column), but also combinations of either of these and W or R seem useful.
          • 
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        • RA, W, OBP, SLG and BA seem normally distributed, most others do not.
          • 
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        • OOBP and OSLG have a very peaked distribution.
          • 
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        • ‘Playoffs’ seems to be categorical and should probably be encoded as such.
          • 
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        Exercise 1: Build a pipeline#
        
-
        Implement a function build_pipeline that does the following:
        
-
          
-
        • Impute missing values by replacing NaN’s with the feature median for numerical features.
          • 
-
        • Encode the categorical features using OneHotEncoding.
          • 
-
        • If the attribute scaling=True, also scale the data using standard scaling.
          • 
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        • Attach the given regression model to the end of the pipeline
          • 
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        def build_pipeline(regressor, numerical, categorical, scaling=False):
-    """ Build a robust pipeline with the given regression model
-    Keyword arguments:
-    regressor -- the regression model
-    categorical -- the list of categorical features
-    scaling -- whether or not to scale the data
-    
-    Returns: a pipeline
-    """
-    pass
-
        
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-
        ### Model solution
-from sklearn.preprocessing import StandardScaler, MinMaxScaler, OneHotEncoder
-from sklearn.pipeline import make_pipeline, Pipeline
-from sklearn.compose import make_column_transformer
-
-def build_pipeline(regressor, categorical, scaling=False):
-    cat_pipe = make_pipeline(OneHotEncoder(sparse=False, handle_unknown='ignore'))
-    num_pipe = make_pipeline(SimpleImputer(strategy='mean'))
-    if scaling:
-        num_pipe.steps.insert(1,["scaler", StandardScaler()]) 
-    transform = make_column_transformer((cat_pipe, categorical), remainder=num_pipe)
-    # Give a name to the regressor so that we can tune it more easily
-    return Pipeline(steps=[('preprocess', transform), ('reg', regressor)])
-
        
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        Exercise 2: Test the pipeline#
        
-
        Test the pipeline by evaluating linear regression (without scaling) on the dataset, using 5-fold cross-validation and \(R^2\). Make sure to run it on the original dataset (‘X’), not the manually cleaned version (‘X_clean’).
        
-
        
-
        
-
        ### Model solution
-from sklearn.model_selection import cross_val_score
-from sklearn.linear_model import LinearRegression
-categorical = ["Team","League"]
-regressor = LinearRegression()
-pipe = build_pipeline(LinearRegression(),categorical)
-scores = cross_val_score(pipe, X, y)
-print("Cross-validated R^2 score for {}: {:.2f}".format(regressor.__class__.__name__, scores.mean()))
-
        
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        Cross-validated R^2 score for LinearRegression: 0.92
-
        
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        Exercise 3: A first benchmark#
        
-
        Evaluate the following algorithms in their default settings, both with and without scaling, and interpret the results:
        
-
          
-
        • Linear regression
          • 
-
        • Ridge
          • 
-
        • Lasso
          • 
-
        • SVM (RBF)
          • 
-
        • RandomForests
          • 
-
        • GradientBoosting
          • 
-
        
-
        
-
        
-
        ### Model solution
-from sklearn.linear_model import LinearRegression, Ridge, Lasso
-from sklearn.ensemble import RandomForestRegressor, GradientBoostingRegressor
-from sklearn.svm import SVR
-from tqdm import tqdm_notebook as tqdm
-
-models = [LinearRegression(), Ridge(), Lasso(), RandomForestRegressor(), GradientBoostingRegressor(), SVR()]
-for m in tqdm(models):
-    pipe = build_pipeline(m,categorical)
-    scores = cross_val_score(pipe, X, y)
-    print("R^2 score for {}: {:.2f}".format(m.__class__.__name__, scores.mean()))
-    pipe = build_pipeline(m,categorical, scaling=True)
-    scores = cross_val_score(pipe, X, y)
-    print("R^2 score for {} (scaled): {:.2f}".format(m.__class__.__name__, scores.mean()))
-
        
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-
        R^2 score for LinearRegression: 0.92
-R^2 score for LinearRegression (scaled): -22898115995987259424768.00
-R^2 score for Ridge: 0.83
-R^2 score for Ridge (scaled): 0.92
-R^2 score for Lasso: 0.81
-R^2 score for Lasso (scaled): 0.92
-R^2 score for RandomForestRegressor: 0.89
-R^2 score for RandomForestRegressor (scaled): 0.89
-R^2 score for GradientBoostingRegressor: 0.91
-R^2 score for GradientBoostingRegressor (scaled): 0.91
-R^2 score for SVR: -0.46
-R^2 score for SVR (scaled): 0.27
-
        
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-
        Discussion#
        
-
        Without scaling: LinearRegression without scaling works better than Ridge and Lasso. The latter two are perhaps overfitting and need to be tuned. RandomForest and GradientBoosting do well (almost as good as LinearRegression), but can still be improven. The SVM performs very badly (worse than simply predicting the mean).
        
-
        Scaling helps performance significantly, except for LinearRegression which now seems to massively overfit. Since scaling also changes the scale of the coefficients, the default hyperparameter settings may just fit better after scaling for Ridge and Lasso, but not for the unregularized LinearRegression. Indeed, if one feature had a very different scale, the corresponding coefficient has to compensate for this, leading to possibly large coefficients and more likely overfitting. Thus, scaling may sometimes act as a regularizer. The SVM improves a lot after scaling but there is still a lot more room for tuning. The tree-based models are, as expected, not affected by scaling.
        
-
        Note: the extremely bad result for scaled linear regression is caused by a single bad train-test split. If we try different splits we get:
        
-
        
-
        
-
        pipe = build_pipeline(LinearRegression(),categorical,scaling=True)
-scores = cross_val_score(pipe, X, y, cv=8)
-print("R^2 score for {}: {:.2f}".format(LinearRegression().__class__.__name__, scores.mean()))
-
        
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-
        R^2 score for LinearRegression: 0.92
-
        
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        Exercise 4: Tuning linear models#
        
-
        Next, visualize the effect of the alpha regularizer for Ridge and Lasso. Vary alpha from 1e-4 to 1e6 and plot the \(R^2\) score as a line plot (one line for each algorithm). Always use scaling. Interpret the results.
        
-
        
-
        
-
        from sklearn.model_selection import GridSearchCV 
-import numpy as np
-import matplotlib.pyplot as plt
-
-grid_alpha = {'reg__alpha': np.logspace(-4, 6, num=50)}
-
-# Build a pipeline and runs a grid search
-def evaluateGrid(regressor, grid, scaling=False):
-    pipe = build_pipeline(regressor, categorical, scaling=scaling)
-    return GridSearchCV(pipe, grid, n_jobs=-1).fit(X, y)
-
-ridge_res = evaluateGrid(Ridge(), grid_alpha, True)
-_=plt.plot([d['reg__alpha'] for d in ridge_res.cv_results_['params']], 
-           ridge_res.cv_results_['mean_test_score'], 'b', label='Ridge')
-lasso_res = evaluateGrid(Lasso(), grid_alpha, True)
-_=plt.plot([d['reg__alpha'] for d in lasso_res.cv_results_['params']], 
-           lasso_res.cv_results_['mean_test_score'], 'r', label='Lasso')
-_=plt.xscale('log')
-_=plt.ylim([0.8, 0.94])
-plt.legend()
-plt.show();
-print("Best result {:.3f} with {}".format(lasso_res.best_score_, lasso_res.best_params_));
-
        
-
        
-
        
-
        
-../_images/430e78898fdffa9df3c7765ea1e0b5d0fe7992d198c454e7df0fa62a298e6b3c.png
-
        Best result 0.927 with {'reg__alpha': 0.11513953993264481}
-
        
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-
        
-
        Discussion#
        
-
        Lasso (red line) finds a slightly better model than Ridge, with an optional alpha of around 0.1 (you may need to zoon in to see it). For values larger than 10, Lasso starts underfitting heavily (it penalizes large coefficients too much), and \(R^2\) drops to 0 (and lower). Ridge is slighlty less sensitive to alpha and only starts overfitting heavily for alpha values of 1000 or larger.
        
-
        
-
        
-
        
-
        Exercise 5: Tuning SVMs#
        
-
        Next, tune the SVM’s C and gamma. You can stay within the 1e-6 to 1e6 range. Plot the \(R^2\) score as a heatmap.
        
-
        
-
        
-
        def heatmap(values, xlabel, ylabel, xticklabels, yticklabels, cmap=None,
-            vmin=None, vmax=None, ax=None, fmt="%0.2f"):
-    if ax is None:
-        ax = plt.gca()
-    # plot the mean cross-validation scores
-    img = ax.pcolor(values, cmap=cmap, vmin=None, vmax=None)
-    img.update_scalarmappable()
-    ax.set_xlabel(xlabel)
-    ax.set_ylabel(ylabel)
-    ax.set_xticks(np.arange(len(xticklabels)) + .5)
-    ax.set_yticks(np.arange(len(yticklabels)) + .5)
-    ax.set_xticklabels(xticklabels)
-    ax.set_yticklabels(yticklabels)
-    ax.set_aspect(1)
-
-    for p, color, value in zip(img.get_paths(), img.get_facecolors(), img.get_array()):
-        x, y = p.vertices[:-2, :].mean(0)
-        if np.mean(color[:3]) > 0.5:
-            c = 'k'
-        else:
-            c = 'w'
-        ax.text(x, y, fmt % value, color=c, ha="center", va="center")
-    return img
-
        
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-
        
-
        def svm_heat(scaling=False):
-    # Run a 2D grid search and build a heatmap with the results
-    grid_svm = {'reg__C': np.logspace(-5, 5, num=6),
-                'reg__gamma': np.logspace(-6, 1, num=6)}
-    svm_res = evaluateGrid(SVR(), grid_svm, scaling=scaling)
-
-    # Reshape and transpose (we want alpha on the x-axes to compare with the previous plot)
-    scores = svm_res.cv_results_['mean_test_score'].reshape(grid_svm['reg__C'].size,
-                                                            grid_svm['reg__gamma'].size).T
-    heatmap(scores, xlabel='C', xticklabels=grid_svm['reg__C'],
-            ylabel='gamma', yticklabels=grid_svm['reg__gamma'], cmap="viridis");
-
-svm_heat()
-
        
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-../_images/c6589b45bb71c23eec2fe71c20271bbf1b701858dc499842d10e54982115e5d0.png
-
        
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-
        Exercise 5b: Tuning SVMs (2)#
        
-
        Redraw the heatmap, but now use scaling. What do you observe?
        
-
        
-
        
-
        svm_heat(scaling=True)
-
        
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-
        
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-../_images/4e74809ca2d209105609e81e9e8f4638ba55758b4c37ad94376fee3bbf306c95.png
-
        
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-
        The tuned SVM yields scores that are identical to the best scores found (0.92 \(R^2\)), but only if we do scaling.
-Without scaling, we get nowhere near that performance, no matter how much we tune.
        
-
        
-
        
-
        Exercise 6: Feature importance#
        
-
        Retrieve the coefficients from the optimized Lasso, Ridge, and the feature importances from the default RandomForest and GradientBoosting models.
-Compare the results. Do the different models agree on which features are important? You will need to map the encoded feature names to the correct coefficients and feature importances.
        
-
        
-
        
-
        # The OneHotEncoder has messed up our attribute names, so we must map features to names again
-# feature_indices_ returns a mapping for the one-hot-encoded features
-fi = lasso_res.best_estimator_.named_steps['preprocess'].named_transformers_['pipeline'].named_steps['onehotencoder'].get_feature_names(input_features=categorical)
-new_names = list(fi)
-new_names.extend(attribute_names[2:])
-
        
-
        
-
        
-
        
-
        
-
        
-
        # We additionally train a RandomForest and Gradient Booster to see if they return the same feature importances
-rf_pipe = build_pipeline(RandomForestRegressor(),categorical)
-rf_pipe.fit(X, y);
-gb_pipe = build_pipeline(GradientBoostingRegressor(),categorical)
-gb_pipe.fit(X, y);
-
        
-
        
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-
        
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-
        
-
        df = pd.DataFrame({'names': new_names, 
-                   'lasso': lasso_res.best_estimator_.get_params()['reg'].coef_,
-                   'ridge': ridge_res.best_estimator_.get_params()['reg'].coef_,
-                   'random_forest': rf_pipe.named_steps.reg.feature_importances_,
-                   'gradient_boosting': gb_pipe.named_steps.reg.feature_importances_})
-ind = np.arange(len(df))
-width = 0.2
-
-# Coefficients
-fig, ax = plt.subplots(figsize=(6, 10))
-ax.barh(ind, df.lasso, width, color='red', label='Lasso')
-ax.barh(ind + width, df.ridge, width, color='green', label='Ridge')
-ax.set_yticklabels(new_names)
-ax.set_yticks(np.arange(len(new_names)))
-ax.set_xlabel('Coefficients')
-ax.legend()
-plt.show()
-
-fig, ax = plt.subplots(figsize=(6, 10))
-# RandomForest feature importances
-ax.barh(ind + width*2, df.random_forest, width, color='orange', label='RandomForest')
-ax.barh(ind + width*3, df.gradient_boosting, width, color='blue', label='GradientBoosting')
-ax.set_yticklabels(new_names)
-ax.set_yticks(np.arange(len(new_names)))
-ax.set_xlabel('Feature importance (RF/GB)')
-ax.set_xlim(-0.285, 0.8) #
-ax.legend()
-plt.show()
-
        
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-../_images/b76d87e106c2b645df2ca06f25b9177a44efa32c5578063d3b7b9125ffbe12ab.png
-../_images/194160ff63fd822f9d77ca2a377ca018d0729d832facef60ca0f4fdafada1708.png
-
        
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-
        Ridge and lasso roughly agree on the importance of features. Especially SLG, OBP, W, and RA are deemed important, and to a lesser degree Year. Also, interestingly, it seems to matter whether the player plays in the American League (League_AL) or not, and playing in some teams (BOSton, BALtimore, NYMets, OAKland) is also a good indicator.
        
-
        One very obvious phenomenon is that Ridge considers all the one-hot-encoded features to be quite important. Since ridge uses the L2 norm, it will prefer many small coefficients, whereas Lasso (L1 norm) prefers to have many coefficients equal to 0. This is exactly what we are seeing here. From the plots above, we’ve seen that Ridge performs worse than Lasso, and the rather large coefficients for one-hot-encoded features hint at overfitting.
        
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        RandomForest and GradientBoosting deem especially SLG and OBP important. All the one-hot-encoded features have an importance of about 0.
        
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        Lab 6: Bayesian models (Solution)#
        
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-
        
-
        
-
        # General imports
-%matplotlib inline
-from preamble import *
-plt.rcParams['figure.dpi'] = 100
-
        
-
        
-
        
-
        
-
        The function to predict and the dataset we create from it:
        
-
        
-
        
-
        def f(x):
-    """The function to predict."""
-    return np.sin((x - 2.5) ** 3)
-
-plt.figure(figsize=(8,4))
-t = np.linspace(0,5,1000)
-plt.plot(t, f(t), 'r', label = 'original f(x)')
-
        
-
        
-
        
-
        
-
        [<matplotlib.lines.Line2D at 0x7fe415cadeb0>]
-
        
-
        
-../_images/3f4b4b671332779dce8b9ef16c08b380620ba300832ece0cabc8e9822049f370.png
-
        
-
        
-
        The dataset we create based on the function:
        
-
        
-
        
-
        # Dataset sampled from a sine function
-rng = np.random.RandomState(4)
-X_ = rng.uniform(0, 5, 1000)[:, np.newaxis]
-y_ = f(X_).ravel()
-
        
-
        
-
        
-
        
-
        
-
        
-
        def plot_gp(g, X_train, y_train, X_full, y_full, y_pred_mean, y_pred_std, use_title="yes"):
-    """
-    Visualizes the GP predictions, training points and original function
-    
-    Attributes:
-    X_train -- The training data
-    y_train -- The correct labels
-    X_full -- The data to calculate predictions
-    y_full -- The correct labels of the prediction data
-    y_pred_mean -- the predicted means
-    y_pred_std -- the predicted st. devs.
-    """
-    x_ = np.linspace(0, 5, 1000)[:,np.newaxis]
-    
-    idx = np.argsort(X_full[:,0])
-    
-    # Original function
-    a = X_full[idx]
-    b = y_full[idx]
-    
-    plt.figure(figsize=(8,4))
-    plt.plot(a, 
-             b, 'r', label = 'original f(x)')
-    
-    # Training points
-    plt.scatter(X_train, y_train, c='r', s=50, zorder=10, edgecolors=(0, 0, 0))
-    
-    # Prediction 
-    d = y_pred_mean[idx]
-    e = y_pred_std[idx]
-    plt.plot(a, d, 'k', lw=1, zorder=9)
-    plt.fill_between(a[:,0], d - 1.96*e, d + 1.96*e, alpha=0.2, color='k')
-    
-    if use_title == "yes":
-        plt.title("Posterior (kernel: %s)\n Log-Likelihood: %.3f"
-              % (g.kernel_, g.log_marginal_likelihood(g.kernel_.theta)),
-              fontsize=12)
-    plt.tight_layout()
-
        
-
        
-
        
-
        
-
        
-
        
-
        Exercise 1: visualizing predictions#
        
-
        Train a GP regressor with a RBF kernel with default hyperparameters on a 1% sample of the sine data. Note that by learning a GP the hyperparameters of the chosen kernel are tuned automatically. To visualize what the GP has learned, use the model to predict values for the entire dataset. Plot the original function, the predictions and the training data points. You can use the function plot_gp() to assist with plotting.
        
-
        
-
        
-
        from sklearn.gaussian_process import GaussianProcessRegressor
-from sklearn.gaussian_process.kernels import (RBF, Matern, RationalQuadratic,
-                                              ExpSineSquared, DotProduct,
-                                              ConstantKernel)
-
-X_train = X_[:10]
-y_train = y_[:10]
-
-kernel = 1.0 * RBF()
-gp = GaussianProcessRegressor(kernel=kernel, n_restarts_optimizer=10)
-
-gp.fit(X_train, y_train)
-
-y_pred_mean, y_pred_std = gp.predict(X_, return_std=True)
-
-plot_gp(gp, X_train, y_train, X_, y_, y_pred_mean, y_pred_std)
-
        
-
        
-
        
-
        
-../_images/4d18942bdb367e78fedf8970c2ad535d6fe635e004ee38f732aeff6059ba2832.png
-
        
-
        
-
        
-
        
-
        Exercise 2: reducing the uncertainty#
        
-
        Fit a model using 5% and 10% of the data. Now try setting n_restarts_optimizer in the GaussianProcessRegressor constructor. Plot the results. What differences do you see?
        
-
        
-
        
-
        X2 = X_[:50]
-y2 = y_[:50]
-
-gp2 = GaussianProcessRegressor(kernel = kernel, n_restarts_optimizer=10)
-gp2.fit(X2, y2)
-y2_pred_mean, y2_pred_std = gp2.predict(X_, return_std=True)
-plot_gp(gp2, X2, y2, X_, y_, y2_pred_mean, y2_pred_std)
-
-X3 = X_[:100]
-y3 = y_[:100]
-
-gp3 = GaussianProcessRegressor(kernel = kernel, n_restarts_optimizer=10)
-
-gp3.fit(X3, y3)
-y3_pred_mean, y3_pred_std = gp3.predict(X_, return_std=True)
-plot_gp(gp3, X3, y3, X_, y_, y3_pred_mean, y3_pred_std)
-
        
-
        
-
        
-
        
-../_images/fa8033d996976607ca6866adbc5265c7def939f5ceb557d8af6b8132bb9b1ba7.png
-../_images/29180bdeaa18a47726476a1b1cf22374405f98ab21b6c20267a996aeeabf4e66.png
-
        
-
        
-
        
-
        
-
        Exercise 3: Kernels#
        
-
        Like SVMs, kernels play a major role in GPs. Using a 5% sample of the data, train one GP  with each of the following kernels:
        
-
          
-
        • RBF
          • 
-
        • RationalQuadratic
          • 
-
        • ExpSineSquared
          • 
-
        • DotProduct
          • 
-
        • Matern
          • 
-
        
-
        What differences do you see in the log-likelihood? Which model fit best the training data?
        
-
        
-
        
-
        kernels = [1.0 * RBF(),
-           1.0 * RationalQuadratic(),
-           1.0 * ExpSineSquared(),
-           DotProduct(),
-           1.0 * Matern()]
-
-for kernel in kernels:
-    gp= GaussianProcessRegressor(kernel=kernel,n_restarts_optimizer=10)
-    gp.fit(X2, y2)
-    y_pred_mean, y_pred_std = gp.predict(X_, return_std=True)
-    plot_gp(gp, X2, y2, X_, y_, y_pred_mean, y_pred_std)
-
        
-
        
-
        
-
        
-../_images/b8d4a6bfe6e7c09f3415dc0dd949d11ebd2c67e28a77f27e7cbaa928ccbe4171.png
-../_images/3af4a0e837a173629dbf24414a9507210fa9e48c8059eb91fefad1e4b1541915.png
-../_images/083402cf4ad8ac77878d0e6d7315f403a75285ae7dd0be5046b864b127eaf80a.png
-../_images/ad991b0bc0319c8179b0fbcab20ded3140d785ea79bc62e0a7ece822c0b73295.png
-../_images/527f99965a8e6cec2b6a7e90b90b794f2386f8a0e3020b3dc89876049f51fca5.png
-
        
-
        
-
        
-
        
-
        Exercise 4: Mauna Loa data#
        
-
        We now look at the problem of predicting the monthly average CO2 concentrations collected at the Mauna Loa Observatory in Hawaii, between 1958 and 2001. This is a time-series data.
        
-
        
-
        
-
        from sklearn.datasets import fetch_openml
-
-# originally from sci-kit learn
-def load_mauna_loa_atmospheric_co2():
-    ml_data = fetch_openml(data_id=41187, as_frame=False)
-    months = []
-    ppmv_sums = []
-    counts = []
-
-    y = ml_data.data[:, 0]
-    m = ml_data.data[:, 1]
-    month_float = y + (m - 1) / 12
-    ppmvs = ml_data.target
-
-    for month, ppmv in zip(month_float, ppmvs):
-        if not months or month != months[-1]:
-            months.append(month)
-            ppmv_sums.append(ppmv)
-            counts.append(1)
-        else:
-            # aggregate monthly sum to produce average
-            ppmv_sums[-1] += ppmv
-            counts[-1] += 1
-
-    months = np.asarray(months).reshape(-1, 1)
-    avg_ppmvs = np.asarray(ppmv_sums) / counts
-    return months, avg_ppmvs
-
-
-X_mauna, y_mauna = load_mauna_loa_atmospheric_co2()
-
        
-
        
-
        
-
        
-
        Quick visualization:
        
-
        
-
        
-
        #Quick visualization
-plt.plot(X_mauna,y_mauna)
-plt.xlabel('date')
-plt.ylabel('co2')
-
        
-
        
-
        
-
        
-
        Text(0, 0.5, 'co2')
-
        
-
        
-../_images/bd4fa4c1478f0e99774409bd841c7be0de3db3ee535ddc0ddb2c970b33df7fc1.png
-
        
-
        
-
        
-
        
-
        Exercise 4.1#
        
-
        Signals like this usually consist of a combination of different “sub-signals”, e.g. a long-term component, a seasonal component, a noise component, and so on. When defining a GP kernel, you can combine multiple kernels, such as:
        
-
          
-
        • A RBF kernel can be used to explain long-term, smooth patterns.
          • 
-
        • The seasonal component can be modeled by an ExpSineSquared component.
          • 
-
        • Small and medium-term irregularities can be modeled by a RationalQuadratic component.
          • 
-
        • WhiteNoise kernel to model white noise.
          • 
-
        
-
        Train a GP using the first 75% data points as training data using the kernel below. Experiment with removing one or more kernels and check the results visually (you can use plot_gp). What do you observe?
        
-
        
-
        
-
        from sklearn.gaussian_process.kernels import WhiteKernel
-
-k1 = 50.0**2 * RBF(length_scale=50.0)  # long term smooth rising trend
-k2 = 2.0**2 * RBF(length_scale=100.0) \
-    * ExpSineSquared(length_scale=1.0, periodicity=1.0,
-                     periodicity_bounds="fixed")  # seasonal component
-# medium term irregularities
-k3 = 0.5**2 * RationalQuadratic(length_scale=1.0, alpha=1.0)
-k4 = 0.1**2 * RBF(length_scale=0.1) \
-    + WhiteKernel(noise_level=0.1**2,
-                  noise_level_bounds=(1e-5, np.inf))  # noise terms
-
-kernel = k1 + k2 +  k3 + k4
-
        
-
        
-
        
-
        
-
        
-
        
-
        end = round(len(X_mauna) * 0.75)
-
-gp = GaussianProcessRegressor(kernel=kernel, normalize_y=True)
-gp.fit(X_mauna[:end], y_mauna[:end])
-
-# Make the prediction on the meshed x-axis (ask for MSE as well)
-y_mean, y_sigma = gp.predict(X_mauna, return_std=True)
-
-plot_gp(gp, X_mauna[:end], y_mauna[:end], X_mauna, y_mauna, y_mean, y_sigma, "no")
-
-print("Learned kernel: \n",gp.kernel)
-
        
-
        
-
        
-
        
-
        Learned kernel: 
- 50**2 * RBF(length_scale=50) + 2**2 * RBF(length_scale=100) * ExpSineSquared(length_scale=1, periodicity=1) + 0.5**2 * RationalQuadratic(alpha=1, length_scale=1) + 0.1**2 * RBF(length_scale=0.1) + WhiteKernel(noise_level=0.01)
-
        
-
        
-../_images/3739925082971225c5fa90b3ec2a22872caeed73879447ac60140116d44d6c84.png
-
        
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-By Joaquin Vanschoren
-
        
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-      © Copyright 2023. CC0 Licensed - Use as you like. Appropriate credit is very welcome.
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        Lab 7: Neural networks
        
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-              
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-                
        
-                  
-  
        
-
        Lab 7: Neural networks#
        
-
        In this lab we will build dense neural networks on the MNIST dataset.
        
-
        Make sure you read the tutorial for this lab first.
        
-
        
-
        Load the data and create train-test splits#
        
-
        
-
        
-
        # Global imports and settings
-%matplotlib inline
-import numpy as np
-import pandas as pd
-import openml as oml
-import os
-import matplotlib.pyplot as plt
-import tensorflow.keras as keras
-print("Using Keras",keras.__version__)
-os.environ['TF_CPP_MIN_LOG_LEVEL'] = "2"
-
        
-
        
-
        
-
        
-
        Using Keras 2.7.0
-
        
-
        
-
        
-
        
-
        
-
        
-
        # Download MNIST data. Takes a while the first time.
-mnist = oml.datasets.get_dataset(554)
-X, y, _, _ = mnist.get_data(target=mnist.default_target_attribute, dataset_format='array');
-X = X.reshape(70000, 28, 28)
-
-# Take some random examples
-from random import randint
-fig, axes = plt.subplots(1, 5,  figsize=(10, 5))
-for i in range(5):
-    n = randint(0,70000)
-    axes[i].imshow(X[n], cmap=plt.cm.gray_r)
-    axes[i].set_xticks([])
-    axes[i].set_yticks([])
-    axes[i].set_xlabel("{}".format(y[n]))
-plt.show();
-
        
-
        
-
        
-
        
-../_images/cc82a7a9ddac27ce50cb7b6aed03a41513ef51f85ef02e2aabb317cf1acb7ecf.png
-
        
-
        
-
        
-
        
-
        # For MNIST, there exists a predefined stratified train-test split of 60000-10000. We therefore don't shuffle or stratify here.
-from sklearn.model_selection import train_test_split
-X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=60000, random_state=0)
-
        
-
        
-
        
-
        
-
        
-
        
-
        Exercise 1: Preprocessing#
        
-
          
-
        • Normalize the data: map each feature value from its current representation (an integer between 0 and 255) to a floating-point value between 0 and 1.0.
          • 
-
        • Store the floating-point values in x_train_normalized and x_test_normalized.
          • 
-
        • Map the class label to a on-hot-encoded value. Store in y_train_encoded and y_test_encoded.
          • 
-
        
-
        
-
        
-
        # Solution
-x_train_normalized = X_train / 255.0
-x_test_normalized = X_test / 255.0
-
-from tensorflow.keras.utils import to_categorical
-y_train_encoded = to_categorical(y_train)
-y_test_encoded = to_categorical(y_test)
-
        
-
        
-
        
-
        
-
        
-
        
-
        Exercise 2: Create a deep neural net model#
        
-
        Implement a create_model function which defines the topography of the deep neural net, specifying the following:
        
-
          
-
        • The number of layers in the deep neural net: Use 2 dense layers for now.
          • 
-
        • The number of nodes in each layer: these are parameters of your function.
          • 
-
        • Any regularization layers. Add at least one dropout layer.
          • 
-
        • The optimizer and learning rate. Make the learning rate a parameter of your function as well.
          • 
-
        
-
        Consider:
        
-
          
-
        • What should be the shape of the input layer?
          • 
-
        • Which activation function you will need for the last layer, since this is a 10-class classification problem?
          • 
-
        
-
        
-
        
-
        ### Create and compile a 'deep' neural net
-def create_model(layer_1_units=32, layer_2_units=10, learning_rate=0.001, dropout_rate=0.3):
-    pass
-
        
-
        
-
        
-
        
-
        
-
        
-
        # Solution
-def create_model(layer_1_units=32, layer_2_units=10, learning_rate=0.001, dropout_rate=0.3):
-
-    model = keras.models.Sequential()
-
-    # The features are stored in a two-dimensional 28X28 array. 
-    # Flatten that two-dimensional array into a a one-dimensional 
-    # 784-element array.
-    model.add(keras.layers.Flatten(input_shape=(28, 28)))
-
-    # Define the first hidden layer.   
-    model.add(keras.layers.Dense(units=32, activation='relu'))
-
-    # Define a dropout regularization layer. 
-    model.add(keras.layers.Dropout(rate=dropout_rate))
-
-    # Define the output layer. The units parameter is set to 10 because
-    # the model must choose among 10 possible output values (representing
-    # the digits from 0 to 9, inclusive).
-    model.add(keras.layers.Dense(units=10, activation='softmax'))     
-
-    # Construct the layers into a model that TensorFlow can execute.  
-    # Notice that the loss function for multi-class classification
-    # is different than the loss function for binary classification.
-    # Using Adam here. RMSProp would also be fine
-    model.compile(optimizer=keras.optimizers.Adam(lr=learning_rate),
-                  loss="categorical_crossentropy", metrics=['accuracy'])
-
-    return model       
-
        
-
        
-
        
-
        
-
        
-
        
-
        Exercise 3: Create a training function#
        
-
        Implement a train_model function which trains and evaluates a given model.
-It should do a train-validation split and report the train and validation loss and accuracy, and return the training history.
        
-
        
-
        
-
        def train_model(model, X, y, validation_split=0.1, epochs=10, batch_size=None):
-    """
-    model: the model to train
-    X, y: the training data and labels
-    validation_split: the percentage of data set aside for the validation set
-    epochs: the number of epochs to train for
-    batch_size: the batch size for minibatch SGD
-    """
-    pass
-
        
-
        
-
        
-
        
-
        
-
        
-
        # Solution
-def train_model(model, X, y, validation_split=0.1, epochs=10, batch_size=None):
-    """
-    model: the model to train
-    X, y: the training data and labels
-    validation_split: the percentage of data set aside for the validation set
-    epochs: the number of epochs to train for
-    batch_size: the batch size for minibatch SGD
-    """
-    X_train, x_val, y_train, y_val = train_test_split(X, y, test_size=validation_split, shuffle=True, stratify=y, random_state=0)
-    
-    history = model.fit(x=X_train, y=y_train, batch_size=batch_size, verbose=0,
-                        epochs=epochs, shuffle=True, validation_data=(x_val, y_val))
-    return history 
-
        
-
        
-
        
-
        
-
        
-
        
-
        Exercise 4: Evaluate the model#
        
-
        Train the model with a learning rate of 0.003, 50 epochs, batch size 4000, and a validation set that is 20% of the total training data.
-Use default settings otherwise. Plot the learning curve of the loss, validation loss, accuracy, and validation accuracy. Finally, report the performance on the test set.
        
-
        Feel free to use the plotting function below, or implement the callback from the tutorial to see results in real time.
        
-
        
-
        
-
        # Helper plotting function
-#
-# history: the history object returned by the fit function
-# list_of_metrics: the metrics to plot
-def plot_curve(history, list_of_metrics):
-    
-    plt.figure()
-    plt.xlabel("Epoch")
-    plt.ylabel("Value")
-
-    epochs = history.epoch
-    hist = pd.DataFrame(history.history)
-
-    for m in list_of_metrics:
-        x = hist[m]
-        plt.plot(epochs[1:], x[1:], label=m, lw=2)
-
-    plt.legend()
-
        
-
        
-
        
-
        
-
        
-
        
-
        # Solution
-# Settings
-learning_rate = 0.003
-epochs = 50
-batch_size = 4000
-validation_split = 0.2
-
-# Create the model the model's topography.
-model = create_model(learning_rate)
-
-# Train the model on the normalized training set.
-history = train_model(model, x_train_normalized, y_train_encoded, 
-                      validation_split, epochs, batch_size)
-
-# Plot a graph of the metric vs. epochs.
-list_of_metrics = ['accuracy','val_accuracy','loss','val_loss']
-plot_curve(history, list_of_metrics)
-
-# Evaluate against the test set.
-print("\n Evaluation on the test set [loss, accuracy]:")
-model.evaluate(x=x_test_normalized, y=y_test_encoded, 
-               batch_size=batch_size, verbose=0)
-
        
-
        
-
        
-
        
-
        Metal device set to: Apple M1 Pro
-
        
-
        
-
        /Users/jvanscho/miniforge3/lib/python3.9/site-packages/keras/optimizer_v2/adam.py:105: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.
-  super(Adam, self).__init__(name, **kwargs)
-
        
-
        
-
         Evaluation on the test set [loss, accuracy]:
-
        
-
        
-
        [0.21780921518802643, 0.9358000159263611]
-
        
-
        
-../_images/f9506f9e6f3971cc5e8159d8ab4130a2d93e96d587cf9444fba0f95cac684e75.png
-
        
-
        
-
        
-
        
-
        Exercise 5: Optimize the model#
        
-
        Try to optimize the model, either manually or with a tuning method. At least optimize the following:
        
-
          
-
        • the number of hidden layers
          • 
-
        • the number of nodes in each layer
          • 
-
        • the amount of dropout layers and the dropout rate
          • 
-
        
-
        Try to reach at least 96% accuracy against the test set.
        
-
        
-
        
-
        # Solution
-# For an example with random search, see the tutorial
-# Here, we search manually, following the following hunches:
-#   * Adding more nodes to the first hidden layer will improve accuracy. The input size is 784, so we should not make it too small
-#   * Adding a second hidden layer generally improves accuracy.
-#   * For larger models (more nodes), we need to regularize more (more dropout)
-
-batch_size = 4000 # Pretty high, but making this smaller doesn't seem to help much.
-epochs = 70
-
-# Create the model the model's topography.
-model = create_model(layer_1_units=800, layer_2_units=800, learning_rate=0.003, dropout_rate= 0.15)
-
-# Train the model on the normalized training set.
-history = train_model(model, x_train_normalized, y_train_encoded, 
-                      validation_split, epochs, batch_size)
-
-# Plot a graph of the metric vs. epochs.
-list_of_metrics = ['accuracy','val_accuracy','loss','val_loss']
-plot_curve(history, list_of_metrics)
-
-# Evaluate against the test set.
-print("\n Evaluation on the test set (accuracy):")
-model.evaluate(x=x_test_normalized, y=y_test_encoded, 
-               batch_size=batch_size, verbose=0)[1]
-
        
-
        
-
        
-
        
-
        /Users/jvanscho/miniforge3/lib/python3.9/site-packages/keras/optimizer_v2/adam.py:105: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.
-  super(Adam, self).__init__(name, **kwargs)
-
        
-
        
-
         Evaluation on the test set (accuracy):
-
        
-
        
-
        0.9571000337600708
-
        
-
        
-../_images/af5246af88ef9e3c99bf3cdd47fe89790b5e954e646f881a8d56f949d130d4d8.png
-
        
-
        
-
        
-
        
-
        # Solution with tuning. Takes a long time, and the best found solution isn't better.
-# The maximum number of nodes was set to 265. Setting it higher may yield better result.
-
-from tensorflow.keras import optimizers
-import keras_tuner as kt
-
-
-def build_model(hp):
-    model = keras.models.Sequential()
-
-    # Tune the number of units in the dense layers
-    hp_units = hp.Int('units', min_value = 32, max_value = 265, step = 32)
-    hp_units2 = hp.Int('units2', min_value = 32, max_value = 265, step = 32)
-    hp_dropout = hp.Float('dropout', min_value = 0.1, max_value = 0.5, step = 0.1)
-
-    model.add(keras.layers.Flatten(input_shape=(28, 28)))
-    model.add(keras.layers.Dense(units = hp_units, activation = 'relu'))
-    model.add(keras.layers.Dropout(rate= hp_dropout))
-    model.add(keras.layers.Dense(units = hp_units2, activation = 'relu'))
-    model.add(keras.layers.Dense(10))
-
-    model.compile(optimizer = 'rmsprop',
-                  loss = 'categorical_crossentropy',
-                  metrics = ['accuracy'])
-    return model
-
-tuner = kt.RandomSearch(build_model, max_trials=5, objective = 'val_accuracy', project_name='mnist_tuning')
-
-X_train, x_val, y_train, y_val = train_test_split(x_train_normalized, y_train_encoded, test_size=0.1, shuffle=True, stratify=y_train_encoded, random_state=0)
-tuner.search(x=X_train, y=y_train, epochs = 50, validation_data = (x_val, y_val), verbose=0)
-
-# Get the optimal hyperparameters
-best_hps = tuner.get_best_hyperparameters(num_trials = 1)[0]
-
        
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-By Joaquin Vanschoren
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-      © Copyright 2023. CC0 Licensed - Use as you like. Appropriate credit is very welcome.
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        Lab 8: Object recognition with convolutional neural networks
        
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-
        Lab 8: Object recognition with convolutional neural networks#
        
-
        In this lab we consider the CIFAR dataset, but model it using convolutional neural networks instead of linear models.
-There is no separate tutorial, but you can find lots of examples in the lecture notebook on convolutional neural networks.
        
-
        Tip: You can run these exercises faster on a GPU (but they will also run fine on a CPU). If you do not have a GPU locally, you can upload this notebook to Google Colab. You can enable GPU support at “runtime” -> “change runtime type”.
        
-
        
-
        
-
        import tensorflow as tf
-import os
-tf.config.experimental.list_physical_devices('GPU') # Check whether GPUs are available
-os.environ['TF_CPP_MIN_LOG_LEVEL'] = "2"
-
        
-
        
-
        
-
        
-
        
-
        
-
        %matplotlib inline
-import openml as oml
-import matplotlib.pyplot as plt
-
        
-
        
-
        
-
        
-
        
-
        
-
        # Download CIFAR data. Takes a while the first time.
-# This version returns 3x32x32 resolution images. 
-# If you feel like it, repeat the exercises with the 96x96x3 resolution version by using ID 41103 
-cifar = oml.datasets.get_dataset(40926) 
-X, y, _, _ = cifar.get_data(target=cifar.default_target_attribute, dataset_format='array'); 
-cifar_classes = {0: "airplane", 1: "automobile", 2: "bird", 3: "cat", 4: "deer",
-                 5: "dog", 6: "frog", 7: "horse", 8: "ship", 9: "truck"}
-
        
-
        
-
        
-
        
-
        
-
        
-
        # The data is in a weird 3x32x32 format, we need to reshape and transpose
-Xr = X.reshape((len(X),3,32,32)).transpose(0,2,3,1)
-
        
-
        
-
        
-
        
-
        
-
        
-
        # Take some random examples, reshape to a 32x32 image and plot
-from random import randint
-fig, axes = plt.subplots(1, 5,  figsize=(10, 5))
-for i in range(5):
-    n = randint(0,len(Xr))
-    # The data is stored in a 3x32x32 format, so we need to transpose it
-    axes[i].imshow(Xr[n]/255)
-    axes[i].set_xlabel((cifar_classes[int(y[n])]))
-    axes[i].set_xticks(()), axes[i].set_yticks(())
-plt.show();
-
        
-
        
-
        
-
        
-../_images/5cd0fac758103966139dcee0c86a484fee4faef93740678145a345e0f143ffd6.png
-
        
-
        
-
        
-
        Exercise 1: A simple model#
        
-
          
-
        • Split the data into 80% training and 20% validation sets
          • 
-
        • Normalize the data to [0,1]
          • 
-
        • Build a ConvNet with 3 convolutional layers interspersed with MaxPooling layers, and one dense layer.
          
-
            
-
          • Use at least 32 filters in the first layer and ReLU activation.
            • 
-
          • Otherwise, make rational design choices or experiment a bit to see what works.
            • 
-
          
-
          • 
-
        • You should at least get 60% accuracy.
          • 
-
        • For training, you can try batch sizes of 64, and 20-50 epochs, but feel free to explore this as well
          • 
-
        • Plot and interpret the learning curves
          • 
-
        
-
        
-
        
-
        from sklearn.model_selection import train_test_split
-X_train, X_test, y_train, y_test = train_test_split(Xr,y, stratify=y, train_size=0.8)
-
        
-
        
-
        
-
        
-
        
-
        
-
        from tensorflow.keras.utils import to_categorical
-X_train = X_train / 255.
-X_test = X_test / 255.
-y_train = to_categorical(y_train)
-y_test = to_categorical(y_test)
-
        
-
        
-
        
-
        
-
        
-
        
-
        from tensorflow.keras import layers
-from tensorflow.keras import models
-
-model = models.Sequential()
-model.add(layers.Conv2D(32, (3, 3), activation='relu', input_shape=(32, 32, 3)))
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Conv2D(64, (3, 3), activation='relu'))
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Conv2D(64, (3, 3), activation='relu'))
-model.add(layers.Flatten())
-model.add(layers.Dense(64, activation='relu'))
-model.add(layers.Dense(10, activation='softmax'))
-model.compile(optimizer='rmsprop',
-              loss='categorical_crossentropy',
-              metrics=['accuracy'])
-history = model.fit(X_train, y_train, epochs=25, batch_size=64, verbose=0,
-                    validation_data=(X_test, y_test))
-
        
-
        
-
        
-
        
-
        Metal device set to: Apple M1 Pro
-
        
-
        
-
        
-
        
-
        
-
        
-
        import pandas as pd
-import numpy as np
-pd.DataFrame(history.history).plot(lw=2,style=['b:','r:','b-','r-']);
-print("Max val_acc",np.max(history.history['val_accuracy']))
-
        
-
        
-
        
-
        
-
        Max val_acc 0.6492500305175781
-
        
-
        
-../_images/6ec37b1351ae0c260a0ccef804a3eb0452935a8ea395cb3b4c60373087fceafd.png
-
        
-
        
-
        Already decent performance but the model starts overfitting heavily after epoch 15.
        
-
        
-
        
-
        Exercise 2: VGG-like model#
        
-
          
-
        • Mimic the VGG model by building 3 ‘blocks’ of 2 convolutional layers each
          • 
-
        • Do MaxPooling after each block
          • 
-
        • The first layer should have at least 32 filters
          • 
-
        • Use zero-padding to be able to build a deeper model
          • 
-
        • Use a dense layer with at least 128 hidden nodes.
          • 
-
        • Plot and interpret the learning curves
          • 
-
        
-
        
-
        
-
        model = models.Sequential()
-model.add(layers.Conv2D(32, (3, 3), activation='relu', padding='same', input_shape=(32, 32, 3)))
-model.add(layers.Conv2D(32, (3, 3), activation='relu', padding='same'))
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Conv2D(64, (3, 3), activation='relu', padding='same'))
-model.add(layers.Conv2D(64, (3, 3), activation='relu', padding='same'))
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Conv2D(128, (3, 3), activation='relu', padding='same'))
-model.add(layers.Conv2D(128, (3, 3), activation='relu', padding='same'))
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Flatten())
-model.add(layers.Dense(128, activation='relu'))
-model.add(layers.Dense(10, activation='softmax'))
-model.compile(optimizer='rmsprop',
-              loss='categorical_crossentropy',
-              metrics=['accuracy'])
-history = model.fit(X_train, y_train, epochs=25, batch_size=64, verbose=0,
-                    validation_data=(X_test, y_test))
-
        
-
        
-
        
-
        
-
        
-
        
-
        pd.DataFrame(history.history).plot(lw=2,style=['b:','r:','b-','r-']);
-print("Max val_acc",np.max(history.history['val_accuracy']))
-
        
-
        
-
        
-
        
-
        Max val_acc 0.6827500462532043
-
        
-
        
-../_images/dd2fbf7d0ca958ff5941d89f3d6656aae6878371962b8a1d524c46205104c92d.png
-
        
-
        
-
        Better result, but still overfitting heavily
        
-
        
-
        
-
        Exercise 3: Regularization#
        
-
          
-
        • Explore different ways to regularize your VGG-like model
          
-
            
-
          • Try adding some dropout after every MaxPooling and Dense layer.
            
-
              
-
            • What are good Dropout rates?
              • 
-
            
-
            • 
-
          • Try batch nornmalization together with Dropout
            • 
-
          
-
          • 
-
        • Plot and interpret the learning curves
          • 
-
        
-
        
-
        
-
        model = models.Sequential()
-model.add(layers.Conv2D(32, (3, 3), activation='relu', padding='same', input_shape=(32, 32, 3)))
-model.add(layers.Conv2D(32, (3, 3), activation='relu', padding='same'))
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Dropout(0.2))
-model.add(layers.Conv2D(64, (3, 3), activation='relu', padding='same'))
-model.add(layers.Conv2D(64, (3, 3), activation='relu', padding='same'))
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Dropout(0.2))
-model.add(layers.Conv2D(128, (3, 3), activation='relu', padding='same'))
-model.add(layers.Conv2D(128, (3, 3), activation='relu', padding='same'))
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Dropout(0.2))
-model.add(layers.Flatten())
-model.add(layers.Dense(128, activation='relu'))
-model.add(layers.Dropout(0.2))
-model.add(layers.Dense(10, activation='softmax'))
-model.compile(optimizer='rmsprop',
-              loss='categorical_crossentropy',
-              metrics=['accuracy'])
-history = model.fit(X_train, y_train, epochs=25, batch_size=64, verbose=0,
-                    validation_data=(X_test, y_test))
-
        
-
        
-
        
-
        
-
        
-
        
-
        pd.DataFrame(history.history).plot(lw=2,style=['b:','r:','b-','r-']);
-print("Max val_acc",np.max(history.history['val_accuracy']))
-
        
-
        
-
        
-
        
-
        Max val_acc 0.7305000424385071
-
        
-
        
-../_images/631f2b8e63972f0c8ed640f9ba510cd3f58c649f316abeb3f288603c946339d3.png
-
        
-
        
-
        Accuracy is quite a bit better and overfitting seems lessened
        
-
        Another common approach is to gradually increase the amount of dropout. This forces layers deep in the model to regularize more than layers closer to the input.
        
-
        
-
        
-
        model = models.Sequential()
-model.add(layers.Conv2D(32, (3, 3), activation='relu', padding='same', input_shape=(32, 32, 3)))
-model.add(layers.Conv2D(32, (3, 3), activation='relu', padding='same'))
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Dropout(0.2))
-model.add(layers.Conv2D(64, (3, 3), activation='relu', padding='same'))
-model.add(layers.Conv2D(64, (3, 3), activation='relu', padding='same'))
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Dropout(0.3))
-model.add(layers.Conv2D(128, (3, 3), activation='relu', padding='same'))
-model.add(layers.Conv2D(128, (3, 3), activation='relu', padding='same'))
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Dropout(0.4))
-model.add(layers.Flatten())
-model.add(layers.Dense(128, activation='relu'))
-model.add(layers.Dropout(0.5))
-model.add(layers.Dense(10, activation='softmax'))
-model.compile(optimizer='rmsprop',
-              loss='categorical_crossentropy',
-              metrics=['accuracy'])
-history = model.fit(X_train, y_train, epochs=25, batch_size=64, verbose=0,
-                    validation_data=(X_test, y_test))
-
        
-
        
-
        
-
        
-
        
-
        
-
        pd.DataFrame(history.history).plot(lw=2,style=['b:','r:','b-','r-']);
-print("Max val_acc",np.max(history.history['val_accuracy']))
-
        
-
        
-
        
-
        
-
        Max val_acc 0.7412500381469727
-
        
-
        
-../_images/126c43a647c246c4904891c216c21612a9f9b2ff730b1172886cac992fbbd848.png
-
        
-
        
-
        Slightly better accuracy and very little overfitting remains.
        
-
        Next, we try adding Batch Normalization.
        
-
        
-
        
-
        model = models.Sequential()
-model.add(layers.Conv2D(32, (3, 3), activation='relu', padding='same', input_shape=(32, 32, 3)))
-model.add(layers.BatchNormalization())
-model.add(layers.Conv2D(32, (3, 3), activation='relu', padding='same'))
-model.add(layers.BatchNormalization())
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Dropout(0.2))
-model.add(layers.Conv2D(64, (3, 3), activation='relu', padding='same'))
-model.add(layers.BatchNormalization())
-model.add(layers.Conv2D(64, (3, 3), activation='relu', padding='same'))
-model.add(layers.BatchNormalization())
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Dropout(0.3))
-model.add(layers.Conv2D(128, (3, 3), activation='relu', padding='same'))
-model.add(layers.BatchNormalization())
-model.add(layers.Conv2D(128, (3, 3), activation='relu', padding='same'))
-model.add(layers.BatchNormalization())
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Dropout(0.4))
-model.add(layers.Flatten())
-model.add(layers.Dense(128, activation='relu'))
-model.add(layers.BatchNormalization())
-model.add(layers.Dropout(0.5))
-model.add(layers.Dense(10, activation='softmax'))
-model.compile(optimizer='rmsprop',
-              loss='categorical_crossentropy',
-              metrics=['accuracy'])
-history = model.fit(X_train, y_train, epochs=25, batch_size=64, verbose=0,
-                    validation_data=(X_test, y_test))
-
        
-
        
-
        
-
        
-
        
-
        
-
        pd.DataFrame(history.history).plot(lw=2,style=['b:','r:','b-','r-']);
-print("Max val_acc",np.max(history.history['val_accuracy']))
-
        
-
        
-
        
-
        
-
        Max val_acc 0.7827500104904175
-
        
-
        
-../_images/73110a91c076f14386e897031949c7bb8e0ab336716f4e392beca56456ac6a10.png
-
        
-
        
-
        
-
        
-
        Exercise 4: Data Augmentation#
        
-
          
-
        • Perform image augmentation. You can use the ImageDataGenerator for this.
          • 
-
        • What is the effect? What is the effect with and without Dropout?
          • 
-
        • Plot and interpret the learning curves
          • 
-
        
-
        
-
        
-
        from tensorflow.keras.preprocessing.image import ImageDataGenerator
-
-train_datagen = ImageDataGenerator(
-    width_shift_range=0.1,
-    height_shift_range=0.1,
-    horizontal_flip=True,)
-it_train = train_datagen.flow(X_train, y_train, batch_size=64)
-
        
-
        
-
        
-
        
-
        
-
        
-
        from tensorflow.keras import layers
-from tensorflow.keras import models
-
-model = models.Sequential()
-model.add(layers.Conv2D(32, (3, 3), activation='relu', padding='same', input_shape=(32, 32, 3)))
-model.add(layers.BatchNormalization())
-model.add(layers.Conv2D(32, (3, 3), activation='relu', padding='same'))
-model.add(layers.BatchNormalization())
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Dropout(0.2))
-model.add(layers.Conv2D(64, (3, 3), activation='relu', padding='same'))
-model.add(layers.BatchNormalization())
-model.add(layers.Conv2D(64, (3, 3), activation='relu', padding='same'))
-model.add(layers.BatchNormalization())
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Dropout(0.3))
-model.add(layers.Conv2D(128, (3, 3), activation='relu', padding='same'))
-model.add(layers.BatchNormalization())
-model.add(layers.Conv2D(128, (3, 3), activation='relu', padding='same'))
-model.add(layers.BatchNormalization())
-model.add(layers.MaxPooling2D((2, 2)))
-model.add(layers.Dropout(0.4))
-model.add(layers.Flatten())
-model.add(layers.Dense(128, activation='relu'))
-model.add(layers.BatchNormalization())
-model.add(layers.Dropout(0.5))
-model.add(layers.Dense(10, activation='softmax'))
-model.compile(optimizer='rmsprop',
-              loss='categorical_crossentropy',
-              metrics=['accuracy'])
-
-steps = int(X_train.shape[0] / 64)
-history = model.fit(it_train, epochs=25, steps_per_epoch=steps, verbose=0,
-                    validation_data=(X_test, y_test))
-
        
-
        
-
        
-
        
-
        
-
        
-
        import pandas as pd
-import numpy as np
-pd.DataFrame(history.history).plot(lw=2,style=['b:','r:','b-','r-']);
-print("Max val_acc",np.max(history.history['val_accuracy']))
-
        
-
        
-
        
-
        
-
        Max val_acc 0.8022500276565552
-
        
-
        
-../_images/4d0e96f82305c43bf0dd9c159249077ff7afbbbcd9bbd9906feb2d469934c7c9.png
-
        
-
        
-
        We get 2-3% improvement. We get the best results with very subtle data augmentation (small shifts and flips). The images are quite low resolution and rotation or sheer will destroy too much information.
        
-
        
-
        
-
        Exercise 5: Interpreting misclassifications#
        
-
        Chances are that even your best models are not yet perfect. It is important to understand what kind of errors it still makes.
        
-
          
-
        • Run the test images through the network and detect all misclassified ones
          • 
-
        • Interpret the results. Are these misclassifications to be expected?
          • 
-
        • Compute the confusion matrix. Which classes are often confused?
          • 
-
        
-
        
-
        
-
        y_pred = model.predict(X_test)
-misclassified_samples = np.nonzero(np.argmax(y_test, axis=1) != np.argmax(y_pred, axis=1))[0]
-
        
-
        
-
        
-
        
-
        Since we have numeric outputs (a value per class), we need to take the class with the maximum value as the predicted class.
        
-
        
-
        
-
        # Visualize the (first five) misclassifications, together with the predicted and actual class
-fig, axes = plt.subplots(1, 5,  figsize=(10, 5))
-for nr, i in enumerate(misclassified_samples[:5]):
-    axes[nr].imshow(X_test[i])
-    axes[nr].set_xlabel("Predicted: %s,\n Actual : %s" % (cifar_classes[np.argmax(y_pred[i])],cifar_classes[np.argmax(y_test[i])]))
-    axes[nr].set_xticks(()), axes[nr].set_yticks(())
-
-plt.show();
-
        
-
        
-
        
-
        
-../_images/8a25833aacb4d8ba2ec988125222c275c6ee44e79314bec95b3d8372df61c2fe.png
-
        
-
        
-
        Some of these are indeed hard to categorize, although we can probably still improve the model quite a bit.
        
-
        
-
        
-
        from sklearn.metrics import confusion_matrix
-cm = confusion_matrix(np.argmax(y_test, axis=1),np.argmax(y_pred, axis=1))
-fig, ax = plt.subplots()
-im = ax.imshow(cm)
-ax.set_xticks(np.arange(10)), ax.set_yticks(np.arange(10))
-ax.set_xticklabels(list(cifar_classes.values()), rotation=45, ha="right")
-ax.set_yticklabels(list(cifar_classes.values()))
-ax.set_ylabel('True')
-ax.set_xlabel('Predicted')
-for i in range(100):
-    ax.text(int(i/10),i%10,cm[i%10,int(i/10)], ha="center", va="center", color="w")
-
        
-
        
-
        
-
        
-../_images/99e10c626f885233b6831a5ea20688e43723b19c6f5bb2f455287cdcaeb91e96.png
-
        
-
        
-
        Most misclassifications seem to involve cats, birds, and horses. The most common misclassification is between cats and dogs.
        
-
        
-
        
-
        Exercise 6: Interpreting the model#
        
-
        Retrain your best model on all the data. Next, retrieve and visualize the activations (feature maps) for every filter for every layer, or at least for a few filters for every layer. Tip: see the course notebooks for examples on how to do this.
        
-
        Interpret the results. Is your model indeed learning something useful?
        
-
        
-
        
-
        model.summary()
-
        
-
        
-
        
-
        
-
        Model: "sequential_5"
-_________________________________________________________________
- Layer (type)                Output Shape              Param #   
-=================================================================
- conv2d_27 (Conv2D)          (None, 32, 32, 32)        896       
-                                                                 
- batch_normalization_7 (Batc  (None, 32, 32, 32)       128       
- hNormalization)                                                 
-                                                                 
- conv2d_28 (Conv2D)          (None, 32, 32, 32)        9248      
-                                                                 
- batch_normalization_8 (Batc  (None, 32, 32, 32)       128       
- hNormalization)                                                 
-                                                                 
- max_pooling2d_14 (MaxPoolin  (None, 16, 16, 32)       0         
- g2D)                                                            
-                                                                 
- dropout_12 (Dropout)        (None, 16, 16, 32)        0         
-                                                                 
- conv2d_29 (Conv2D)          (None, 16, 16, 64)        18496     
-                                                                 
- batch_normalization_9 (Batc  (None, 16, 16, 64)       256       
- hNormalization)                                                 
-                                                                 
- conv2d_30 (Conv2D)          (None, 16, 16, 64)        36928     
-                                                                 
- batch_normalization_10 (Bat  (None, 16, 16, 64)       256       
- chNormalization)                                                
-                                                                 
- max_pooling2d_15 (MaxPoolin  (None, 8, 8, 64)         0         
- g2D)                                                            
-                                                                 
- dropout_13 (Dropout)        (None, 8, 8, 64)          0         
-                                                                 
- conv2d_31 (Conv2D)          (None, 8, 8, 128)         73856     
-                                                                 
- batch_normalization_11 (Bat  (None, 8, 8, 128)        512       
- chNormalization)                                                
-                                                                 
- conv2d_32 (Conv2D)          (None, 8, 8, 128)         147584    
-                                                                 
- batch_normalization_12 (Bat  (None, 8, 8, 128)        512       
- chNormalization)                                                
-                                                                 
- max_pooling2d_16 (MaxPoolin  (None, 4, 4, 128)        0         
- g2D)                                                            
-                                                                 
- dropout_14 (Dropout)        (None, 4, 4, 128)         0         
-                                                                 
- flatten_5 (Flatten)         (None, 2048)              0         
-                                                                 
- dense_10 (Dense)            (None, 128)               262272    
-                                                                 
- batch_normalization_13 (Bat  (None, 128)              512       
- chNormalization)                                                
-                                                                 
- dropout_15 (Dropout)        (None, 128)               0         
-                                                                 
- dense_11 (Dense)            (None, 10)                1290      
-                                                                 
-=================================================================
-Total params: 552,874
-Trainable params: 551,722
-Non-trainable params: 1,152
-_________________________________________________________________
-
        
-
        
-
        
-
        
-
        
-
        
-
        from tensorflow.keras import models
-
-img_tensor = X_test[4]
-img_tensor = np.expand_dims(img_tensor, axis=0) 
-
-# Extracts the outputs of the top 8 layers:
-layer_outputs = [layer.output for layer in model.layers[:15]]
-# Creates a model that will return these outputs, given the model input:
-activation_model = models.Model(inputs=model.input, outputs=layer_outputs)
-
-# This will return a list of 5 Numpy arrays:
-# one array per layer activation
-activations = activation_model.predict(img_tensor)
-
        
-
        
-
        
-
        
-
        
-
        
-
        plt.rcParams['figure.dpi'] = 120
-first_layer_activation = activations[0]
-
-f, (ax1, ax2) = plt.subplots(1, 2, sharey=True)
-ax1.imshow(img_tensor[0])
-ax2.matshow(first_layer_activation[0, :, :, 2], cmap='viridis')
-ax1.set_xticks([])
-ax1.set_yticks([])
-ax2.set_xticks([])
-ax2.set_yticks([])
-ax1.set_xlabel('Input image')
-ax2.set_xlabel('Activation of filter 2');
-
        
-
        
-
        
-
        
-../_images/d8334313d2ea420b16b72d0ccdcb3e63beb1bcbacc1bfbe9d0c7f88b0206b198.png
-
        
-
        
-
        
-
        
-
        images_per_row = 16
-
-layer_names = []
-for layer in model.layers[:15]:
-    layer_names.append(layer.name)
-
-def plot_activations(layer_index, activations):
-    start = layer_index
-    end = layer_index+1
-    # Now let's display our feature maps
-    for layer_name, layer_activation in zip(layer_names[start:end], activations[start:end]):
-        # This is the number of features in the feature map
-        n_features = layer_activation.shape[-1]
-
-        # The feature map has shape (1, size, size, n_features)
-        size = layer_activation.shape[1]
-
-        # We will tile the activation channels in this matrix
-        n_cols = n_features // images_per_row
-        display_grid = np.zeros((size * n_cols, images_per_row * size))
-
-        # We'll tile each filter into this big horizontal grid
-        for col in range(n_cols):
-            for row in range(images_per_row):
-                channel_image = layer_activation[0,
-                                                 :, :,
-                                                 col * images_per_row + row]
-                # Post-process the feature to make it visually palatable
-                channel_image -= channel_image.mean()
-                channel_image /= channel_image.std()
-                channel_image *= 64
-                channel_image += 128
-                channel_image = np.clip(channel_image, 0, 255).astype('uint8')
-                display_grid[col * size : (col + 1) * size,
-                             row * size : (row + 1) * size] = channel_image
-
-        # Display the grid
-        scale = 1. / size
-        plt.figure(figsize=(scale * display_grid.shape[1],
-                            scale * display_grid.shape[0]))
-        plt.title("Activation of layer {} ({})".format(layer_index+1,layer_name))
-        plt.grid(False)
-        plt.imshow(display_grid, aspect='auto', cmap='viridis')
-
-    plt.show()
-
        
-
        
-
        
-
        
-
        
-
        
-
        plot_activations(0, activations);
-
        
-
        
-
        
-
        
-
        /var/folders/0t/5d8ttqzd773fy0wq3h5db0xr0000gn/T/ipykernel_34025/2702396986.py:30: RuntimeWarning: invalid value encountered in true_divide
-  channel_image /= channel_image.std()
-
        
-
        
-../_images/6d2e74dfbd8c7e93d5ed4f6b27739aae995e92e4daa717584cc09998e85ea81f.png
-
        
-
        
-
        
-
        
-
        plot_activations(2, activations);
-
        
-
        
-
        
-
        
-../_images/a272da1091f9844fabe7354e5f331cfdd3fb162b05dc592914384a683e3d24f2.png
-
        
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-
        
-
        
-
        plot_activations(6, activations);
-
        
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-
        
-../_images/e9d1042a17161cf6ce477252343017f080f1f1bf0d35db4a0994cbec019ee34c.png
-
        
-
        
-
        
-
        
-
        plot_activations(8, activations)
-
        
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-
        
-../_images/b50f7ff96c4de5defdb554c3b88e6a5f3181f5fe04027a8d5bb378c044bb795c.png
-
        
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-
        
-
        plot_activations(12, activations)
-
        
-
        
-
        
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-
        /var/folders/0t/5d8ttqzd773fy0wq3h5db0xr0000gn/T/ipykernel_34025/2702396986.py:30: RuntimeWarning: invalid value encountered in true_divide
-  channel_image /= channel_image.std()
-
        
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-../_images/3f9ba637c5a5feea99676318929e0dd5666970e19352ee90d62fbc0fad83972b.png
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        Optional: Take it a step further#
        
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-By Joaquin Vanschoren
-
        
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-      © Copyright 2023. CC0 Licensed - Use as you like. Appropriate credit is very welcome.
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        Lab 9: Neural Networks for text
        
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        Lab 9: Neural Networks for text#
        
-
        
-
        
-
        # Global imports and settings
-%matplotlib inline
-import numpy as np
-import pandas as pd
-import openml as oml
-import os
-import matplotlib.pyplot as plt
-import tensorflow.keras as keras
-print("Using Keras",keras.__version__)
-os.environ['TF_CPP_MIN_LOG_LEVEL'] = "2"
-
        
-
        
-
        
-
        
-
        Using Keras 2.2.4-tf
-
        
-
        
-
        
-
        
-
        Before you start, read the Tutorial for this lab (‘Deep Learning with Python’)
        
-
        
-
        Exercise 1: Sentiment Analysis#
        
-
          
-
        • Take the IMDB dataset from keras.datasets with 10000 words and the default train-test-split
          • 
-
        
-
        
-
        
-
        from tensorflow.keras.datasets import imdb
-# Download IMDB data with 10000 most frequent words
-word_index = imdb.get_word_index()
-(train_data, train_labels), (test_data, test_labels) = imdb.load_data(num_words=10000)
-reverse_word_index = dict([(value, key) for (key, value) in word_index.items()])
-
-for i in [0,5,10]:
-    print("Review {}:".format(i),' '.join([reverse_word_index.get(i - 3, '?') for i in train_data[i]][0:20]))
-
        
-
        
-
        
-
        
-
        Review 0: ? this film was just brilliant casting location scenery story direction everyone's really suited the part they played and you
-Review 5: ? begins better than it ends funny that the russian submarine crew ? all other actors it's like those scenes
-Review 10: ? french horror cinema has seen something of a revival over the last couple of years with great films such
-
        
-
        
-
        
-
        
-
          
-
        • Vectorize the reviews using one-hot-encoding (see tutorial for helper code)
          • 
-
        
-
        
-
        
-
        # Custom implementation of one-hot-encoding
-def vectorize_sequences(sequences, dimension=10000):
-    results = np.zeros((len(sequences), dimension))
-    for i, sequence in enumerate(sequences):
-        results[i, sequence] = 1.  # set specific indices of results[i] to 1s
-    return results
-x_train = vectorize_sequences(train_data)
-x_test = vectorize_sequences(test_data)
-print("Encoded review: ", train_data[0][0:10])
-print("One-hot-encoded review: ", x_train[0][0:10])
-
-# Convert 0/1 labels to float
-y_train = np.asarray(train_labels).astype('float32')
-y_test = np.asarray(test_labels).astype('float32')
-
-print("Label: ", y_train[0])
-
        
-
        
-
        
-
        
-
        Encoded review:  [1, 14, 22, 16, 43, 530, 973, 1622, 1385, 65]
-One-hot-encoded review:  [0. 1. 1. 0. 1. 1. 1. 1. 1. 1.]
-Label:  1.0
-
        
-
        
-
        
-
        
-
          
-
        • Build a network of 2 Dense layers with 16 nodes each and the ReLU activation function.
          • 
-
        • Use cross-entropy as the loss function, Adagrad as the optimizer, and accuracy as the evaluation matric.
          • 
-
        
-
        
-
        
-
        from tensorflow.keras import models
-from tensorflow.keras import layers 
-
-model = models.Sequential()
-model.add(layers.Dense(16, activation='relu', input_shape=(10000,)))
-model.add(layers.Dense(16, activation='relu'))
-model.add(layers.Dense(1, activation='sigmoid'))
-
-model.compile(optimizer='RMSprop',
-              loss='binary_crossentropy',
-              metrics=['accuracy'])
-
        
-
        
-
        
-
        
-
          
-
        • Plot the learning curves, using the first 10000 samples as the validation set and the rest as the training set.
          • 
-
        • Use 20 epochs and a batch size of 512
          • 
-
        
-
        
-
        
-
        x_val, partial_x_train = x_train[:10000], x_train[10000:]
-y_val, partial_y_train = y_train[:10000], y_train[10000:] 
-history = model.fit(partial_x_train, partial_y_train,
-                    epochs=20, batch_size=512, verbose=0,
-                    validation_data=(x_val, y_val))
-
        
-
        
-
        
-
        
-
        
-
        
-
        # Plotting
-pd.DataFrame(history.history).plot(lw=2);
-
        
-
        
-
        
-
        
-../_images/eacb5482b291355731a0a072f8964a59752038c222796cb8c157c365ff357cdd.png
-
        
-
        
-
        
-
        
-
        from tensorflow.keras import models
-from tensorflow.keras import layers 
-
-model = models.Sequential()
-model.add(layers.Dense(16, activation='relu', input_shape=(10000,)))
-model.add(layers.Dense(16, activation='relu'))
-model.add(layers.Dense(1, activation='sigmoid'))
-
-model.compile(optimizer='RMSprop',
-              loss='binary_crossentropy',
-              metrics=['accuracy'])
-
        
-
        
-
        
-
        
-
          
-
        • Retrain the model, this time using early stopping to stop training at the optimal time
          • 
-
        
-
        
-
        
-
        # Based on the figure, we should stop after 4 epochs
-model.fit(x_train, y_train, epochs=4, batch_size=512, verbose=0)
-result = model.evaluate(x_test, y_test)
-print("Loss: {:.4f}, Accuracy:  {:.4f}".format(*result))
-
        
-
        
-
        
-
        
-
        25000/25000 [==============================] - 2s 100us/sample - loss: 0.2879 - accuracy: 0.8862
-Loss: 0.2879, Accuracy:  0.8862
-
        
-
        
-
        
-
        
-
          
-
        • Try to manually improve the score and explain what you observe. E.g. you could:
          
-
            
-
          • Try 3 hidden layers
            • 
-
          • Change to a higher learning rate (e.g. 0.4)
            • 
-
          • Try another optimizer (e.g. Adagrad)
            • 
-
          • Use more or fewer hidden units (e.g. 64)
            • 
-
          • tanh activation instead of ReLU
            • 
-
          
-
          • 
-
        
-
        
-
        
-
        # Three hidden layers
-# Not really worth it, very similar results
-# Overfits even faster
-model = models.Sequential()
-model.add(layers.Dense(16, activation='relu', input_shape=(10000,)))
-model.add(layers.Dense(16, activation='relu'))
-model.add(layers.Dense(16, activation='relu'))
-model.add(layers.Dense(1, activation='sigmoid'))
-model.compile(optimizer='rmsprop', loss='binary_crossentropy', metrics=['accuracy'])
-history = model.fit(partial_x_train, partial_y_train,
-                    epochs=20, batch_size=512, verbose=0,
-                    validation_data=(x_val, y_val))
-pd.DataFrame(history.history).plot(lw=2);
-
        
-
        
-
        
-
        
-../_images/9f04808c1c84c4798068fb46d511848e08677b1fe27a4eb8430b594547887d7a.png
-
        
-
        
-
        
-
        
-
        # Set the learning rate to 0.1 and plot the learning curves again.
-# learning rate 0.4 gives very high losses which don't plot nicely
-# For high learning rates there is no  convergence, the loss actually increases
-from tensorflow.keras import optimizers
-
-model = models.Sequential()
-model.add(layers.Dense(16, activation='relu', input_shape=(10000,)))
-model.add(layers.Dense(16, activation='relu'))
-model.add(layers.Dense(1, activation='sigmoid'))
-
-model.compile(optimizer=optimizers.RMSprop(lr=0.1),
-              loss='binary_crossentropy',
-              metrics=['accuracy'])
-history = model.fit(partial_x_train, partial_y_train,
-                    epochs=10, batch_size=512, verbose=0,
-                    validation_data=(x_val, y_val))
-
        
-
        
-
        
-
        
-
        
-
        
-
        pd.DataFrame(history.history).plot(lw=2);
-
        
-
        
-
        
-
        
-../_images/6e2f5d86d6d65f6256d4efbe17e0ffb24a9bb356bce1673034f906a7f0d54bd3.png
-
        
-
        
-
        
-
        
-
        # Adagrad optimizer
-# Seems more well-behaved but slower. The validation loss is still decreasing after 20 epochs.
-model = models.Sequential()
-model.add(layers.Dense(16, activation='relu', input_shape=(10000,)))
-model.add(layers.Dense(16, activation='relu'))
-model.add(layers.Dense(16, activation='relu'))
-model.add(layers.Dense(1, activation='sigmoid'))
-model.compile(optimizer='adagrad', loss='binary_crossentropy', metrics=['accuracy'])
-history = model.fit(partial_x_train, partial_y_train,
-                    epochs=20, batch_size=512, verbose=0,
-                    validation_data=(x_val, y_val))
-pd.DataFrame(history.history).plot(lw=2);
-
        
-
        
-
        
-
        
-../_images/0ec2e37f44b238c63ec8c200a71325d21b0e407131ee10e2e2bc7b9e017bab01.png
-
        
-
        
-
        
-
        
-
        # Score is not better than RMSprop with early stopping, but could still improve with more epochs
-result = model.evaluate(x_test, y_test)
-print("Loss: {:.4f}, Accuracy:  {:.4f}".format(*result))
-
        
-
        
-
        
-
        
-
        25000/25000 [==============================] - 3s 114us/sample - loss: 0.3511 - accuracy: 0.8770
-Loss: 0.3511, Accuracy:  0.8770
-
        
-
        
-
        
-
        
-
          
-
        • Further tune the results by doing a grid search for the most interesting hyperparameters
          
-
            
-
          • Tune the learning rate between 0.001 and 1
            • 
-
          • Tune the number of epochs between 1 and 20
            • 
-
          • Use only 3-4 values for each
            • 
-
          
-
          • 
-
        
-
        
-
        
-
        from tensorflow.keras.wrappers.scikit_learn import KerasClassifier, KerasRegressor
-from sklearn.model_selection import GridSearchCV
-
-def make_model(learning_rate=0.01):
-    model = models.Sequential()
-    model.add(layers.Dense(16, activation='relu', input_shape=(10000,)))
-    model.add(layers.Dense(16, activation='relu'))
-    model.add(layers.Dense(1, activation='sigmoid'))
-
-    model.compile(optimizer=optimizers.Adagrad(lr=learning_rate),
-                  loss='binary_crossentropy',
-                  metrics=['accuracy'])
-    return model
-
-clf = KerasClassifier(make_model)
-param_grid = {'epochs': [1, 10, 20],  # epochs is a fit parameter
-              'learning_rate': [0.001, 0.01, 1], # this is a make_model parameter
-              'verbose' : [0]}
-grid = GridSearchCV(clf, param_grid=param_grid, cv=3, return_train_score=True)
-grid.fit(x_train, y_train)
-
        
-
        
-
        
-
        
-
        GridSearchCV(cv=3, error_score=nan,
-             estimator=<tensorflow.python.keras.wrappers.scikit_learn.KerasClassifier object at 0x134b7e0f0>,
-             iid='deprecated', n_jobs=None,
-             param_grid={'epochs': [1, 10, 20],
-                         'learning_rate': [0.001, 0.01, 1], 'verbose': [0]},
-             pre_dispatch='2*n_jobs', refit=True, return_train_score=True,
-             scoring=None, verbose=0)
-
        
-
        
-
        
-
        
-
        Grid search results
        
-
        
-
        
-
        res = pd.DataFrame(grid.cv_results_)
-res.pivot_table(index=["param_epochs", "param_learning_rate"],
-                values=['mean_train_score', "mean_test_score"])
-
        
-
        
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-  
-
        mean_test_scoremean_train_score
        param_epochsparam_learning_rate
        11.00e-030.640.65
        1.00e-020.860.88
        1.00e+000.500.50
        101.00e-030.860.88
        1.00e-020.880.98
        1.00e+000.500.50
        201.00e-030.870.90
        1.00e-020.871.00
        1.00e+000.500.50
        
-
        
-
        
-
        
-
        
-
        Exercise 2: Topic classification#
        
-
          
-
        • Take the Reuters dataset from keras.datasets with 10000 words and the default train-test-split
          • 
-
        
-
        
-
        
-
        from keras.datasets import reuters
-
-(train_data, train_labels), (test_data, test_labels) = reuters.load_data(num_words=10000)
-word_index = reuters.get_word_index()
-reverse_word_index = dict([(value, key) for (key, value) in word_index.items()])
-
-for i in [0,5,10]:
-    print("News wire {}:".format(i),
-          ' '.join([reverse_word_index.get(i - 3, '?') for i in train_data[i]]))
-    # Note that our indices were offset by 3
-
        
-
        
-
        
-
        
-
        Using TensorFlow backend.
-
        
-
        
-
        News wire 0: ? ? ? said as a result of its december acquisition of space co it expects earnings per share in 1987 of 1 15 to 1 30 dlrs per share up from 70 cts in 1986 the company said pretax net should rise to nine to 10 mln dlrs from six mln dlrs in 1986 and rental operation revenues to 19 to 22 mln dlrs from 12 5 mln dlrs it said cash flow per share this year should be 2 50 to three dlrs reuter 3
-News wire 5: ? the u s agriculture department estimated canada's 1986 87 wheat crop at 31 85 mln tonnes vs 31 85 mln tonnes last month it estimated 1985 86 output at 24 25 mln tonnes vs 24 25 mln last month canadian 1986 87 coarse grain production is projected at 27 62 mln tonnes vs 27 62 mln tonnes last month production in 1985 86 is estimated at 24 95 mln tonnes vs 24 95 mln last month canadian wheat exports in 1986 87 are forecast at 19 00 mln tonnes vs 18 00 mln tonnes last month exports in 1985 86 are estimated at 17 71 mln tonnes vs 17 72 mln last month reuter 3
-News wire 10: ? period ended december 31 shr profit 11 cts vs loss 24 cts net profit 224 271 vs loss 511 349 revs 7 258 688 vs 7 200 349 reuter 3
-
        
-
        
-
        
-
        
-
          
-
        • We have to vectorize the data and the labels using one-hot-encoding
          • 
-
        
-
        
-
        
-
        from keras.utils.np_utils import to_categorical
-x_train = vectorize_sequences(train_data)
-x_test = vectorize_sequences(test_data)
-one_hot_train_labels = to_categorical(train_labels)
-one_hot_test_labels = to_categorical(test_labels)
-
        
-
        
-
        
-
        
-
          
-
        • Build a network with 2 dense layers of 64 nodes each
          • 
-
        • Make sensible choices about the activation functions, loss, …
          • 
-
        
-
        
-
        
-
        model = models.Sequential()
-model.add(layers.Dense(64, activation='relu', input_shape=(10000,)))
-model.add(layers.Dense(64, activation='relu'))
-model.add(layers.Dense(46, activation='softmax'))
-model.compile(optimizer='rmsprop',
-              loss='categorical_crossentropy',
-              metrics=['accuracy'])
-
        
-
        
-
        
-
        
-
          
-
        • Take a validation set from the first 1000 points of the training set
          • 
-
        • Fit the model with 20 epochs and a batch size of 512
          • 
-
        • Plot the learning curves
          • 
-
        
-
        
-
        
-
        x_val, partial_x_train = x_train[:1000], x_train[1000:]
-y_val, partial_y_train = one_hot_train_labels[:1000], one_hot_train_labels[1000:]
-
        
-
        
-
        
-
        
-
        
-
        
-
        history = model.fit(partial_x_train,
-                    partial_y_train,
-                    epochs=20, verbose=0,
-                    batch_size=512,
-                    validation_data=(x_val, y_val))
-
        
-
        
-
        
-
        
-
        
-
        
-
        pd.DataFrame(history.history).plot(lw=2);
-
        
-
        
-
        
-
        
-../_images/93c1fdf060ed07e4e21f3b8801d481ab0aefded1fa39900c9b64065e3ab9669a.png
-
        
-
        
-
          
-
        • Create an information bottleneck: rebuild the model, but now use only 4 hidden units in the second layer. Evaluate the model. Does it still perform well?
          • 
-
        
-
        
-
        
-
        model = models.Sequential()
-model.add(layers.Dense(64, activation='relu', input_shape=(10000,)))
-model.add(layers.Dense(4, activation='relu'))
-model.add(layers.Dense(46, activation='softmax'))
-
-model.compile(optimizer='rmsprop',
-              loss='categorical_crossentropy',
-              metrics=['accuracy'])
-model.fit(partial_x_train,
-          partial_y_train,
-          epochs=20,
-          batch_size=128, verbose=0,
-          validation_data=(x_val, y_val))
-result = model.evaluate(x_test, one_hot_test_labels)
-print("Loss: {:.4f}, Accuracy: {:.4f}".format(*result))
-
        
-
        
-
        
-
        
-
        2246/2246 [==============================] - 0s 88us/sample - loss: 2.0950 - accuracy: 0.6901
-Loss: 2.0950, Accuracy: 0.6901
-
        
-
        
-
        
-
        
-
        
-
        
-
        Exercise 3: Regularization#
        
-
          
-
        • Go back to the IMDB dataset
          • 
-
        • Retrain with only 4 units per layer
          • 
-
        • Plot the results. What do you observe?
          • 
-
        
-
        
-
        
-
        from keras.datasets import imdb
-import numpy as np
-
-(train_data, train_labels), (test_data, test_labels) = imdb.load_data(num_words=10000)
-
-def vectorize_sequences(sequences, dimension=10000):
-    # Create an all-zero matrix of shape (len(sequences), dimension)
-    results = np.zeros((len(sequences), dimension))
-    for i, sequence in enumerate(sequences):
-        results[i, sequence] = 1.  # set specific indices of results[i] to 1s
-    return results
-
-# Our vectorized training data
-x_train = vectorize_sequences(train_data)
-# Our vectorized test data
-x_test = vectorize_sequences(test_data)
-# Our vectorized labels
-y_train = np.asarray(train_labels).astype('float32')
-y_test = np.asarray(test_labels).astype('float32')
-
        
-
        
-
        
-
        
-
        
-
        
-
        original_model = models.Sequential()
-original_model.add(layers.Dense(16, activation='relu', input_shape=(10000,)))
-original_model.add(layers.Dense(16, activation='relu'))
-original_model.add(layers.Dense(1, activation='sigmoid'))
-
-original_model.compile(optimizer='rmsprop',
-                       loss='binary_crossentropy',
-                       metrics=['acc'])
-
-smaller_model = models.Sequential()
-smaller_model.add(layers.Dense(4, activation='relu', input_shape=(10000,)))
-smaller_model.add(layers.Dense(4, activation='relu'))
-smaller_model.add(layers.Dense(1, activation='sigmoid'))
-
-smaller_model.compile(optimizer='rmsprop',
-                      loss='binary_crossentropy',
-                      metrics=['acc'])
-original_hist = original_model.fit(x_train, y_train,
-                                   epochs=20,
-                                   batch_size=512, verbose=0,
-                                   validation_data=(x_test, y_test))
-smaller_model_hist = smaller_model.fit(x_train, y_train,
-                                       epochs=20,
-                                       batch_size=512, verbose=0,
-                                       validation_data=(x_test, y_test))
-
        
-
        
-
        
-
        
-
        The smaller model starts overfitting later than the original one, and it overfits more slowly
        
-
        
-
        
-
        epochs = range(1, 21)
-original_val_loss = original_hist.history['val_loss']
-smaller_model_val_loss = smaller_model_hist.history['val_loss']
-
        
-
        
-
        
-
        
-
        
-
        
-
        plt.plot(epochs, original_val_loss, 'b+', label='Original model')
-plt.plot(epochs, smaller_model_val_loss, 'bo', label='Smaller model')
-plt.xlabel('Epochs')
-plt.ylabel('Validation loss')
-plt.legend()
-
-plt.show()
-
        
-
        
-
        
-
        
-../_images/858ac9119a5a762e37460c21698ca91fc439ce4844d5a19d95a553ccd78d6529.png
-
        
-
        
-
          
-
        • Use 16 hidden nodes in the layers again, but now add weight regularization. Use L2 loss with alpha=0.001. What do you observe?
          • 
-
        
-
        
-
        
-
        from keras import regularizers
-
-l2_model = models.Sequential()
-l2_model.add(layers.Dense(16, kernel_regularizer=regularizers.l2(0.001),
-                          activation='relu', input_shape=(10000,)))
-l2_model.add(layers.Dense(16, kernel_regularizer=regularizers.l2(0.001),
-                          activation='relu'))
-l2_model.add(layers.Dense(1, activation='sigmoid'))
-
        
-
        
-
        
-
        
-
        
-
        
-
        l2_model.compile(optimizer='rmsprop',
-                 loss='binary_crossentropy',
-                 metrics=['acc'])
-
        
-
        
-
        
-
        
-
        
-
        
-
        l2_model_hist = l2_model.fit(x_train, y_train,
-                             epochs=20,
-                             batch_size=512, verbose=0,
-                             validation_data=(x_test, y_test))
-
        
-
        
-
        
-
        
-
        L2 regularized model is much more resistant to overfitting, even though both have the same number of parameters
        
-
        
-
        
-
        l2_model_val_loss = l2_model_hist.history['val_loss']
-
-plt.plot(epochs, original_val_loss, 'b+', label='Original model')
-plt.plot(epochs, l2_model_val_loss, 'bo', label='L2-regularized model')
-plt.xlabel('Epochs')
-plt.ylabel('Validation loss')
-plt.legend()
-
-plt.show()
-
        
-
        
-
        
-
        
-../_images/dd6a64ce8847a27a63d34bd648a3257d0e1699d8f3bfdae78d30677ed8b89245.png
-
        
-
        
-
          
-
        • Add a drop out layer after every dense layer. Use a dropout rate of 0.5. What do you observe?
          • 
-
        
-
        dpt_model = models.Sequential()
-dpt_model.add(layers.Dense(16, activation='relu', input_shape=(10000,)))
-dpt_model.add(layers.Dropout(0.5))
-dpt_model.add(layers.Dense(16, activation='relu'))
-dpt_model.add(layers.Dropout(0.5))
-dpt_model.add(layers.Dense(1, activation='sigmoid'))
-
-dpt_model.compile(optimizer='rmsprop',
-                  loss='binary_crossentropy',
-                  metrics=['acc'])
-
        
-
        
-
        
-
        
-
        dpt_model = models.Sequential()
-dpt_model.add(layers.Dense(16, activation='relu', input_shape=(10000,)))
-dpt_model.add(layers.Dropout(0.5))
-dpt_model.add(layers.Dense(16, activation='relu'))
-dpt_model.add(layers.Dropout(0.5))
-dpt_model.add(layers.Dense(1, activation='sigmoid'))
-
-dpt_model.compile(optimizer='rmsprop',
-                  loss='binary_crossentropy',
-                  metrics=['acc'])
-
        
-
        
-
        
-
        
-
        
-
        
-
        dpt_model_hist = dpt_model.fit(x_train, y_train,
-                               epochs=20,
-                               batch_size=512, verbose=0,
-                               validation_data=(x_test, y_test))
-
        
-
        
-
        
-
        
-
        Dropout finds a better model, and overfits more slowly as well
        
-
        
-
        
-
        dpt_model_val_loss = dpt_model_hist.history['val_loss']
-
-plt.plot(epochs, original_val_loss, 'b+', label='Original model')
-plt.plot(epochs, dpt_model_val_loss, 'bo', label='Dropout-regularized model')
-plt.xlabel('Epochs')
-plt.ylabel('Validation loss')
-plt.legend()
-
-plt.show()
-
        
-
        
-
        
-
        
-../_images/ce76eabf926094000e9b95de03eab8745f00402b07968867e9ef7fdf18711aa6.png
-
        
-
        
-
        
-
        
-
        Exercise 4: Word embeddings#
        
-
          
-
        • Instead of one-hot-encoding, use a word embedding of length 300
          • 
-
        • Only add an output layer after the embedding.
          • 
-
        • Evaluate as before. Does it perform better?
          • 
-
        
-
        
-
        
-
        from tensorflow.keras.layers import Embedding, Flatten, Dense
-
-max_length = 20 # pad documents to a maximum number of words
-vocab_size = 10000 # vocabulary size
-embedding_length = 300 # vocabulary size
-# define the model
-model = models.Sequential()
-model.add(Embedding(vocab_size, embedding_length, input_length=max_length))
-model.add(Flatten())
-model.add(Dense(1, activation='sigmoid'))
-# compile the mode
-model.compile(optimizer='rmsprop', loss='binary_crossentropy', metrics=['accuracy'])
-# summarize the model
-print(model.summary())
-
        
-
        
-
        
-
        
-
        Model: "sequential_39"
-_________________________________________________________________
-Layer (type)                 Output Shape              Param #   
-=================================================================
-embedding (Embedding)        (None, 20, 300)           3000000   
-_________________________________________________________________
-flatten (Flatten)            (None, 6000)              0         
-_________________________________________________________________
-dense_119 (Dense)            (None, 1)                 6001      
-=================================================================
-Total params: 3,006,001
-Trainable params: 3,006,001
-Non-trainable params: 0
-_________________________________________________________________
-None
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-              
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-By Joaquin Vanschoren
-
        
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-      © Copyright 2023. CC0 Licensed - Use as you like. Appropriate credit is very welcome.
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diff --git a/search.html b/search.html
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--- a/search.html
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@@ -202,6 +202,7 @@
 
 
 
+
      • Lab 2 Tutorial: Model Selection in scikit-learn
        • 
 
      • Lab 4 Tutorial: Data engineering pipelines
        • 
 
      • Lab 6 Tutorial: Deep Learning with TensorFlow
        • 
 
      • Lab 7 Tutorial: Deep Learning for text
        • 
diff --git a/searchindex.js b/searchindex.js
index 3b6fc3678..8097de48e 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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22, 23, 26, 27, 28, 30, 31, 35, 36, 44], "new": [1, 2, 3, 4, 9, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 44], "handbook": 2, "take": [2, 4, 5, 9, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 31, 32, 36, 37, 38, 40, 41, 43, 44], "definit": [2, 21, 29, 41], "whirlwind": [2, 29], "tour": [2, 29], "step": [2, 4, 14, 15, 18, 20, 23, 25, 26, 27, 28, 29, 30, 31, 35, 36, 37, 43, 44], "approach": [2, 18, 20, 22, 24, 25, 27, 28, 29, 32, 37, 43], "try": [2, 3, 4, 5, 7, 9, 12, 13, 16, 17, 22, 24, 26, 28, 29, 30, 36, 37, 38, 41, 42, 43], "datacamp": [2, 3, 29, 31], "intro": [2, 3, 29, 34], "some": [2, 4, 5, 7, 10, 11, 12, 13, 14, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 34, 35, 36, 37, 38, 39, 40, 41, 44], "hackerrank": [2, 29], "challeng": [2, 8, 29, 41], "window": [2, 22, 27, 28, 31, 32], "user": [2, 3, 18, 19, 22, 31], "anaconda": [2, 32], "prompt": 2, "command": [2, 27, 29], "lab": [2, 23, 31, 32], "mac": 2, "termin": 2, 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17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44], "g": [2, 4, 5, 8, 10, 11, 12, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42], "fancyimput": 2, "custom": [2, 7, 15, 19, 27, 28, 30], "possibl": [2, 6, 7, 14, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 31, 33, 35, 37, 44], "highli": [2, 3, 24, 31, 37], "avoid": [2, 14, 19, 20, 22, 23, 24, 26, 27, 29, 36], "interfer": 2, "other": [2, 3, 4, 5, 6, 8, 10, 11, 14, 17, 19, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 39, 40, 41, 43, 44], "project": [2, 14, 17, 19, 20, 21, 22, 25, 28, 31, 37], "class": [2, 3, 5, 7, 9, 13, 14, 16, 18, 19, 20, 21, 23, 24, 25, 26, 28, 31, 32, 33, 36, 38, 39, 40], "strictli": [2, 20], "fresh": 2, "sinc": [1, 2, 4, 5, 10, 13, 14, 15, 20, 21, 22, 25, 27, 28, 34, 35, 36, 37, 38, 39, 43, 44], "automat": [2, 6, 11, 12, 19, 20, 31], "call": [2, 3, 4, 5, 7, 8, 11, 14, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 36, 39, 44], "mlcours": 2, "whatev": [2, 30], "n": [2, 3, 5, 6, 11, 12, 13, 14, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 42, 43, 44], "activ": [2, 13, 15, 16, 17, 18, 20, 25, 28], "deactic": 2, "deactiv": 2, "venv": 2, "prefer": [2, 14, 18, 20, 22, 24, 26, 35], "sourc": [2, 8, 30, 32], "bin": [2, 3, 22, 23, 28, 30, 43], "script": [2, 34, 38], "type": [2, 3, 5, 9, 14, 15, 16, 18, 20, 22, 24, 26, 27, 28, 30, 31, 32, 36, 37, 41], "haven": 2, "instruct": [2, 34], "ubuntu": [2, 32], "even": [2, 4, 16, 18, 21, 23, 24, 26, 27, 28, 31, 36, 37, 38, 40, 41, 43], "setup": [2, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 32, 33, 37], "easili": [2, 6, 20, 23, 24, 25, 28, 30, 31, 32, 33, 36, 41, 42], "git": [2, 19, 20, 21, 22, 23, 24, 25, 26, 27, 32, 33], "repositori": 2, "gui": [2, 30], "http": [2, 7, 8, 10, 11, 14, 15, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 35, 39, 40, 41, 42], "com": 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41, 43], "path": [2, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 32, 33, 37], "txt": [2, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 32, 33], "upgrad": 2, "u": [2, 3, 14, 17, 20, 21, 24, 25, 42], "option": [2, 3, 5, 10, 22, 23, 24, 25, 28, 29, 30, 31, 32, 35, 37], "should": [2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 31, 35, 36, 37, 38, 39, 40, 41, 43, 44], "our": [2, 3, 5, 7, 8, 11, 14, 15, 17, 18, 19, 20, 21, 22, 25, 26, 27, 28, 31, 35, 36, 37, 38, 41, 44], "interleav": 2, "document": [2, 3, 5, 7, 9, 15, 18, 23, 24, 28, 31, 34, 37], "markdown": [2, 18], "execut": [2, 31, 32], "browser": 2, "That": [2, 25], "mean": [2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15, 18, 19, 20, 22, 23, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 43, 44], "re": [2, 9, 14, 22, 23, 24, 25, 27, 40, 44], "quick": [2, 7, 8, 10, 12, 29, 30, 39], "depth": [2, 9, 19, 23, 26, 32, 39], "check": [2, 4, 5, 7, 8, 12, 18, 19, 23, 26, 30, 35, 36, 37], "cell": [2, 3, 18, 26, 28, 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diff --git a/studies/S9 Multi-fidelity optimization.html b/studies/S9 Multi-fidelity optimization.html
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--- a/studies/S9 Multi-fidelity optimization.html	
+++ b/studies/S9 Multi-fidelity optimization.html	
@@ -203,6 +203,7 @@
 
 
 
+
      • Lab 2 Tutorial: Model Selection in scikit-learn
        • 
 
      • Lab 4 Tutorial: Data engineering pipelines
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      • Lab 6 Tutorial: Deep Learning with TensorFlow
        • 
 
      • Lab 7 Tutorial: Deep Learning for text
        •