Logistic Regression#
Bid Ideas#
Let \((x_1,y_1),\dots,(x_N,y_N)\) be a dataset such that the target values are binary: \(y_k = 0\) or \(1\) for all \(k=1,\dots,N\). The goal of logistic regression is to construct a logistic function \(\sigma(x;W,b)\) which best fits the data by minimizing a cost function such as cross entropy. The logistic regression model \(\sigma(x;W,b)\) takes values in the interval \((0,1)\) and we use the function to classify new data \(x\) by assigning the target \(y=0\) if \(\sigma(x,W,b) < 1/2\) and \(y = 1\) if \(\sigma(x;W,b) > 1/2\). The hyperplane \(\sigma(x;W,b) = 1/2\) defines the decision boundary.
Learning Goals#
Summarize properties of the logistic function and the weight and bias parameters
Compare and contrast cost functions for logistic regression models such as mean least squares and cross entropy
Implement regularization terms in cost functions and tune regularization parameters
Approximate optimal model parameters for logistic regression models using
sklearn