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lrCostFunction.m
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lrCostFunction.m
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function [J, grad] = lrCostFunction(theta, X, y, lambda)
%LRCOSTFUNCTION Compute cost and gradient for logistic regression with
%regularization
% J = LRCOSTFUNCTION(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
%
% Hint: The computation of the cost function and gradients can be
% efficiently vectorized. For example, consider the computation
%
% sigmoid(X * theta)
%
% Each row of the resulting matrix will contain the value of the
% prediction for that example. You can make use of this to vectorize
% the cost function and gradient computations.
%
% Hint: When computing the gradient of the regularized cost function,
% there're many possible vectorized solutions, but one solution
% looks like:
% grad = (unregularized gradient for logistic regression)
% temp = theta;
% temp(1) = 0; % because we don't add anything for j = 0
% grad = grad + YOUR_CODE_HERE (using the temp variable)
%
n = size(X,2);
h = sigmoid(X*theta);
% Cost function (apenas seguindo a formula)
J = ( (-y)' *log(h)-(1-y)' * log(1-h))/m;
% excluindo o theta0 - devemos ignorar o Theta0 na regularizacao
theta1 = [0 ; theta(2:size(theta), :)];
% somatorio do lambda - REGULARIZATION
soma = sum(theta1'*theta1);
% penalty pra cada feature
p = (lambda*soma) / (2*m);
% J + penalty
J = J + p;
% grad.. a formula eh (1/m SOMATORIO ( (h0(x) - y) * X + lambda ).. para j >= 1
% para j == 0 nao devemos considerar a soma com lambda
% (por isso zeramos a primera posicao do theta1)
grad = ( X' * (h - y) + lambda*theta1 ) / m;
% =============================================================
end