Exercise 2 Part 1

sigmoid.m

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

% You need to return the following variables correctly
g = zeros(size(z));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the sigmoid of each value of z (z can be a matrix,
% vector or scalar).

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));

% ====================== 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
%
% Note: grad should have the same dimensions as theta
%

z = theta’ * X’;

J = sum( -y .* (log(sigmoid(z)))’ – (1 – y).* (log(1 – sigmoid(z)))’) * 1/m;

grad = 1/m * (sigmoid(z)’ – 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);

% ====================== YOUR CODE HERE ======================
% Instructions: Complete the following code to make predictions using
% your learned logistic regression parameters.
% You should set p to a vector of 0’s and 1’s
%
result = sigmoid(theta’ * X’);
for counter = 1:size(result,2)
if(result(counter) >= 0.5)
p(counter) = 1;
else
p(counter) = 0;
endif
endfor

% =========================================================================
end