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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)
- %
- % exclude the first term
- rt = lambda / (2 * m) * sum((theta(2:end) .^ 2));
- J = 1/m * sum(-y .* log(sigmoid(X * theta)) - (1 .- y) .* log(1 .- sigmoid(X * theta))) ...
- + rt;
- % regularized mask
- rm = [zeros(1,1); theta(2:end)];
- grad = 1/m * X' * (sigmoid(X * theta) .- y) + lambda/m .* rm;
-
- % =============================================================
- grad = grad(:);
- end
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