Week # 3, Regularization

Can anyone please explain why the summation i = 1 to n is taken care while finding the derivative? For expression without regularization, the summation i = 1 to m appears in derivative equation but summation i = 1 to n is not appearing. I know derivative of w^2 is 2w but why the summation sign for i = 1 to n has disappeared?

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The notation here is a little tricky.

The first cost equation (one on top) uses the w variable as a matrix, and the summation there refers to summing up all the params inside the w matrix. It’s the general equation of cost that applies to all the params (including w).

On the other hand, the derivative equation (down below) is with respect to a single param w_j inside w. The derivative (with respect to w_j) of all the other params in w that is not w_j is 0, and so they sum up to 0. The only term that is not 0 is the derivative of w_j, and so that is the only term you are seeing.

Thank you for explanation. I understand better now. :smiley: