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z8^Nleo3L@1zP_4a8#VXwh5z8BVmsvuq{{*maxY%*fxwFkAyu|z!bzTEMboqVG1Jo zh=e^>!xY30EMbq?ezxFXWGfQ(SPL_l;z!tHJuC-CE+b)&S75m?MVGM0CRiDaOh>{V zn_=ZJ#ab%z6<}ggnft3otQ%oZLw4I={wc<`2c?#J1Z8y?=`%||(JlRm!a2Y@SF++D z4I^fS&ANpee}yrG(=-9G6Sn`vi5q2&4?^vrn zOSP&6!oH;@mb5ys)Z4F%d}ygp8?-vI)RT9#I=0l`Y3*8_SUTsGR;QM3exx8?M5-*^ z^Cs3OND4_KOdro2@E diff --git a/docs/equations/pymle-equations.tex b/docs/equations/pymle-equations.tex index 9c416b05..061ca7b1 100644 --- a/docs/equations/pymle-equations.tex +++ b/docs/equations/pymle-equations.tex @@ -12,7 +12,7 @@ \title{Python Machine Learning\\ Equation Reference} \author{Sebastian Raschka \\ \texttt{mail@sebastianraschka.com}} -\date{ \vspace{2cm} 05\slash 04\slash 2015 (last updated: 06\slash 15\slash 2016) \\\begin{flushleft} \vspace{2cm} \noindent\rule{10cm}{0.4pt} \\ Code Repository and Resources:: \href{https://github.com/rasbt/python-machine-learning-book}{https://github.com/rasbt/python-machine-learning-book} \vspace{2cm} \endgraf @book\{raschka2015python,\\ +\date{ \vspace{2cm} 05\slash 04\slash 2015 (last updated: 06\slash 19\slash 2016) \\\begin{flushleft} \vspace{2cm} \noindent\rule{10cm}{0.4pt} \\ Code Repository and Resources:: \href{https://github.com/rasbt/python-machine-learning-book}{https://github.com/rasbt/python-machine-learning-book} \vspace{2cm} \endgraf @book\{raschka2015python,\\ title=\{Python Machine Learning\},\\ author=\{Raschka, Sebastian\},\\ year=\{2015\},\\ @@ -333,12 +333,13 @@ \subsection{Minimizing cost functions with gradient descent} \begin{split} & \frac{\partial J}{\partial w_j} = \frac{\partial}{\partial w_j} \frac{1}{2} \sum_i \bigg( y^{(i)} - \phi \big( z^{(i)} \big) \bigg)^2 \\ & = \frac{1}{2} \frac{\partial}{\partial w_j} \sum_i \bigg( y^{(i)} - \phi \big( z^{(i)} \big) \bigg)^2 \\ -& = \frac{1}{2} \sum_i 2 \bigg( y^{(i)} - \phi \big( z^{(i)} \big) \bigg) \frac{\partial J}{\partial w_j} \Bigg( y^{(i)} - \sum_i \bigg( w_{j}^{(i)} x_{j}^{(i)} \bigg)\Bigg) \\ +& = \frac{1}{2} \sum_i 2 \big( y^{(i)} - \phi(z^{(i)})\big) \frac{\partial}{\partial w_j} \Big( y^{(i)} - \phi({z^{(i)}}) \Big) \\ +& = \sum_i \big( y^{(i)} - \phi (z^{(i)}) \big) \frac{\partial}{\partial w_j} \Big( y^{(i)} - \sum_i \big(w^{(i)}_{j} x^{(i)}_{j} \big) \Big) \\ & = \sum_i \bigg( y^{(i)} - \phi \big( z^{(i)} \big) \bigg) \bigg( - x_{j}^{(i)} \bigg) \\ & = - \sum_i \bigg( y^{(i)} - \phi \big( z^{(i)} \big) \bigg) x_{j}^{(i)} \\ \end{split} \end{equation*} - +? Performing a matrix-vector multiplication is similar to calculating a vector dot product where each row in the matrix is treated as a single row vector. This vectorized approach represents a more compact notation and results in a more efficient computation using NumPy. For example: \[ @@ -409,7 +410,7 @@ \subsection{Logistic regression intuition and conditional probabilities} event. The term positive event does not necessarily mean good, but refers to the event that we want to predict, for example, the probability that a patient has a certain disease; we can think of the positive event as class label $y =1$. We can then further define the logit function, which is simply the logarithm of the odds ratio (log-odds): \[ -logit(p) = log \frac{p}{1-p} +logit(p) = \log \frac{p}{1-p} \] The logit function takes input values in the range 0 to 1 and transforms them to values over the entire real number range, which we can use to express a linear relationship between feature values and the log-odds: @@ -1180,6 +1181,35 @@ \section{Summary} +%%%%%%%%%%%%%%% +% CHAPTER 6 +%%%%%%%%%%%%%%% + +\chapter{Learning Best Practices for Model Evaluation and Hyperparameter Tuning} + +\section{Streamlining workflows with pipelines} +\subsection{Loading the Breast Cancer Wisconsin dataset} +\subsection{Combining transformers and estimators in a pipeline} +\section{Using k-fold cross-validation to assess model performance} +\subsection{The holdout method} +\subsection{K-fold cross-validation} +\section{Debugging algorithms with learning and validation curves} +\subsection{Diagnosing bias and variance problems with learning curves} +\subsection{Addressing overfitting and underfitting with validation curves} +\section{Fine-tuning machine learning models via grid search} +\subsection{Tuning hyperparameters via grid search} +\subsection{Algorithm selection with nested cross-validation} +\section{Looking at different performance evaluation metrics} +\subsection{Reading a confusion matrix} +\subsection{Optimizing the precision and recall of a classification model} + +\[ +ERR = \frac{FP + FN}{FP + FN + TP + TN} +\] + +\subsection{Plotting a receiver operating characteristic} +\subsection{The scoring metrics for multiclass classification} +\section{Summary} \newpage