eq upd

docs/equations/pymle-equations.tex

@@ -12,7 +12,7 @@
 
 \title{Python Machine Learning\\ Equation Reference}
 \author{Sebastian Raschka \\ \texttt{[email protected]}} 
-\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