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-   Chapter 3 - The Linear Model (http://book.caltech.edu/bookforum/forumdisplay.php?f=110)
-   -   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.

Quote:

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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