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Problem set 3, compute the gradient for a cost function

Hello,

I don’t see that the provided solution gives us the behavior that we would expect. When we introduce the diagonal matrix many ‘features’ in X will be lost because they are multiplied with 0. And this is not what the indices notation shows.

How can I see that the solution (eq. 5) makes sense?

2DF936AD-C426-4612-9452-711E18A81A1C.jpeg

17734B9D-6AB5-49ED-B11C-DEDEA4E29A13.jpeg

And for the same question part D. I don’t really buy the answer because if we have y = 100 and y_hat = 1, we will have very small loss and the function will not be sensitive to outliers (and it will not really take the relative error into account as claimed in the exercise)

4ADB5707-E175-4137-BD69-2A1A468D8C28.jpeg

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