Coursera: Machine Learning Andrew NG-(Week 3) [Assignment Solution]

These solutions are for reference only.

try to solve on your own

but if you get stuck in between than you can refer these solutions

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plotData.m

function plotData(X, y)
%PLOTDATA Plots the data points X and y into a new figure 
%   PLOTDATA(x,y) plots the data points with + for the positive examples
%   and o for the negative examples. X is assumed to be a Mx2 matrix.

% Create New Figure
figure; hold on;

% Find Indices of Positive and Negative Examples
pos = find(y == 1); neg = find(y == 0);
% Plot Examples
plot(X(pos, 1), X(pos, 2), 'k+','LineWidth', 2, ...
'MarkerSize', 7);
plot(X(neg, 1), X(neg, 2), 'ko', 'MarkerFaceColor', 'y', ...
'MarkerSize', 7);

hold off;

end

sigmoid.m

function g = sigmoid(z)
%SIGMOID Compute sigmoid functoon
%   J = SIGMOID(z) computes the sigmoid of z.

g = 1 ./ (1 + exp(-z));

end

costFunction.m

function [J, grad] = costFunction(theta, X, y)
%COSTFUNCTION Compute cost and gradient for logistic regression
%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
%   parameter for 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));

h_theta = sigmoid(X*theta);
J = (1 / m) * ((-y' * log(h_theta)) - (1 - y)' * log(1 - h_theta));

grad = (1 / m) * (h_theta - y)' * X;
end

predict.m

function p = predict(theta, X)
%PREDICT Predict whether the label is 0 or 1 using learned logistic 
%regression parameters theta
%   p = PREDICT(theta, X) computes the predictions for X using a 
%   threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)

m = size(X, 1); % Number of training examples

% You need to return the following variables correctly
p = zeros(m, 1);

p = sigmoid(X * theta) >= 0.5;

end

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));

h_theta = sigmoid(X*theta);
J = (1/m) * (-y' * log(h_theta) - (1-y)' * log(1-h_theta)) + (lambda/(2*m)) * (theta(2:length(theta)))' * theta(2:length(theta));

thetaZero = theta;
thetaZero(1) = 0;

grad = ((1 / m) * (h_theta - y)' * X) + lambda / m * thetaZero';
end