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- 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));
- % ====================== 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
- %J = 1 / m * ((-1 .* y') * log(sigmoid(X * theta)) - (1 .- y)' * log(1 .- sigmoid(X * theta))) %...
- %+ lambda / (2 * m) * [0; (theta([2, rows(theta)],:) .^ 2)];
-
-
- J = 1 / m * sum(((-1 .* y') * log(sigmoid(X * theta)) - (1 .- y)' * log(1 .- sigmoid(X * theta)))) ...
- + lambda / (2 * m) * sum(theta([2: rows(theta)]) .^ 2);
- %size(J)
- %
- % the dumb way
- % first attempt:
- % two step process: compute j0 without regularization and then j1-n with regularization
- % 1. set up a matrix X1 of the same size as X. Next copy the row values from the first column of X into the matrix X1
- % and fill the rest of the rows/columns with zeros. Apply the gradient formula,
- % Use X as the parameter in the sigmoid function
- % this result in an 1x1 matrix
- % 2. set up a 2nd matrix X2N. It contains 0 in its first column, and data copied from col2 to col end of X
- % apply the graident function
- % this result in a 28x1 matrix
- % finally,
- % discard the first row of gradient X2N in Step 2 as it contains the regularized value
- % return the gradient by adding the first result and X2N[2:end]
- %
- %
- %
- X1 = [X(:, 1) zeros(m, columns(X) - 1)];
- grad1 = 1 / m * X1' * (sigmoid(X * theta) - y);
- %fprintf ('grad1: %f\n', grad1);
- X2N = [[zeros(m, 1)] X(:, 2:end)];
- %X2N
- grad2N = 1 / m * X2N' * (sigmoid(X * theta) - y) + lambda / m * theta;
- %grad2N
- grad = [grad1(1, 1); grad2N(2:end, 1)];
- %fprintf ('------------> %f\n', grad(1:5));
- %
- %
- % the quick way
- %
- %
- %grad =1/m * X' * (sigmoid(X* theta) - y) + lambda/m * theta .* [0; ones(length(theta)-1, 1)];
- %fprintf ('------------> %f\n', grad(1:5));
- % =============================================================
- end
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