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-   -   Problem 3.6(a) (http://book.caltech.edu/bookforum/showthread.php?t=4775)

tikenn 07-12-2017 06:41 PM

Problem 3.6(a)
I think this is similar to the answer provided for problem 3.5, but I am having a difficult time understanding why, in Problem 3.4, the error is continuous and differentiable at the point y_n\textbf{w}^T\textbf{x}_n=1. I have the three cases looking like this so far:

y_n\textbf{w}^T\textbf{x}_n>1 in which I believe E(\mathbf{x}_n) = 0
y_n\textbf{w}^T\textbf{x}_n<1 in which I believe E(\mathbf{x}_n) = (1 - y_n\textbf{w}^T\textbf{x}_n)^2
y_n\textbf{w}^T\textbf{x}_n=1 in which I believe E(\mathbf{x}_n) = 0

These cases would make y_n\textbf{w}^T\textbf{x}_n=1 non-differentiable because the derivatives from the left and right are different. Am I evaluating the error from the book wrong --> e_n(\textbf{w})=(\max(0,1-y_n\textbf{w}^T\textbf{x}_n))^2?

htlin 07-15-2017 03:27 PM

Re: Problem 3.6(a)
Are the derivatives on the two sides really different? :-)

tikenn 07-16-2017 01:36 AM

Re: Problem 3.6(a)
I apologize, I realize I made an error in labeling the problem that my question refers to. My original question actually refers to Problem 3.4a.


Originally Posted by htlin (Post 12709)
Are the derivatives on the two sides really different? :-)

Anyway, thank you for the hint! My confusion was with how problem 3.5 and problem 3.4 were so different, but I forgot to evaluate the gradients all the way through for both. Thanks!

subbupd 08-24-2017 06:05 AM

Re: Problem 3.6(a)
Correct - evaluating the gradients would work!

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