Regularized logistic regression - Gradient calculation
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Hello, I am doing a regularized logistic regression task and stuck with the partial derivatives. The gradient should be normalized (added lambda/m*theta), except for the first term theta(1). So, I had the following code, which works incorrectly:
grad(1) = 1/m*((sigmoid(X(:,1)*theta(1))-y)'*X(:,1));
grad(2:end) = 1/m*((sigmoid(X(:,2:end)*theta(2:end))-y)'*X(:,2:end))' + lambda/m*theta(2:end);
Finally, I came to another solution, which works fine:
grad = (1/m*(sigmoid(X*theta)-y)'*X)';
temp = theta;
temp(1) =0;
grad = grad + lambda/m*temp;
Can someone please explain, why the first option is incorrect. Thanks a lot!
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Xinwei LONG
2020년 2월 18일
Hi,
I initially wrote the same form of vectoriztion in dealing with cost function and gradients.
Here's what I found out the right answers:
grad(1)=(1/m)*sum(((sigmoid(X*theta)-y).*X(:,1)),1);
grad(2:end)=(1/m)*sum(((sigmoid(X*theta)-y).*X(:,2:end)),1)'+(lambda/m)*theta(2:end);
Please find the differences in inputs of sigmoid function. The gradient equation for theta_0 and other thetas still required the same input in sigmoid function.
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