CostFunction.m

function [J, grad] = costFunction(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
h = sigmoid(theta,X);
cost = -y .* log(h) - (1 - y) .* log(1 - h);
thetaExcludingZero = [ [ 0 ]; theta([2:length(theta)]) ];
J = (1 / m) * sum(cost) + (lambda / (2 * m)) * sum(thetaExcludingZero .^ 2);
grad = (1 / m) .* (X' * (h - y)) + (lambda / m) * thetaExcludingZero;
% =============================================================
end