Exercise 2 Part 2 (Regularization)

costFunctionReg.m

function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
% J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
% theta as the parameter for regularized logistic regression and the
% gradient of the cost w.r.t. to the parameters.

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
% You should set J to the cost.
% Compute the partial derivatives and set grad to the partial
% derivatives of the cost w.r.t. each parameter in theta

J = (1/m)*sum(-y.*log(sigmoid(X*theta)) .-(1.-y).*log(1-sigmoid(X*theta))) + ((lambda/(2*m))*sum(theta(2:end).^2));
grad = 1/m * ((sigmoid(X*theta) .- y)’ * X)’;

grad(2:end) = grad(2:end) + lambda/m * theta(2:end);

% =============================================================

end