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5/data science/r/12/mlclass-ex3/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)
+%
+
+
+h = sigmoid(X * theta);
+base = - y .* log(h) - (1 - y) .* log(1 - h);
+J = 1 / m * sum(base, 1);
+grad_ = 1 / m * (X' * (h - y));
+
+J = J + lambda / (2 * m) * (theta' * theta);
+grad = grad_ + theta * lambda / m;
+grad(1) = grad_(1);
+
+
+
+
+
+
+
+% =============================================================
+
+end