LFD Book Forum

LFD Book Forum (http://book.caltech.edu/bookforum/index.php)
-   Homework 2 (http://book.caltech.edu/bookforum/forumdisplay.php?f=131)
-   -   Minimizing Ein by differentiation wr.t w (http://book.caltech.edu/bookforum/showthread.php?t=4447)

blunderboy 10-17-2013 10:22 PM

Minimizing Ein by differentiation wr.t w
 
https://dl.dropboxusercontent.com/u/...ection_008.png

Can somebody please explain me how we got X' (X' is X Transpose) outside the braces after differentiation. Shouldn't it be X instead of X'.

When I revisited the lecture, I recalled professor saying it is not actually square. It is just transpose multipled by itself. This concept is not clear to me..

Appreciate the help :)

yaser 10-18-2013 12:34 AM

Re: Minimizing Ein by differentiation wr.t w
 
Quote:

Originally Posted by blunderboy (Post 11580)
https://dl.dropboxusercontent.com/u/...ection_008.png

Can somebody please explain me how we got X' (X' is X Transpose) outside the braces after differentiation. Shouldn't it be X instead of X'.

When I revisited the lecture, I recalled professor saying it is not actually square. It is just transpose multipled by itself. This concept is not clear to me..

Appreciate the help :)

This comes from matrix calculus. The quantity || {\rm X}{\bf w}-{\bf y}||^2 is in fact ({\rm X}{\bf w}-{\bf y})^{\rm T} ({\rm X}{\bf w}-{\bf y}).

The squared matrix I referred to was {\rm X^T X}.

blunderboy 10-18-2013 05:45 AM

Re: Minimizing Ein by differentiation wr.t w
 
Aah..Got it. Thank you professor. I really appreciate the quick help from you. Your presence in the forum really help us. Thanks a lot!!:D

yaser 10-18-2013 11:46 AM

Re: Minimizing Ein by differentiation wr.t w
 
Quote:

Originally Posted by blunderboy (Post 11583)
Aah..Got it. Thank you professor. I really appreciate the quick help from you. Your presence in the forum really help us. Thanks a lot!!:D

You are most welcome.


All times are GMT -7. The time now is 12:28 PM.

Powered by vBulletin® Version 3.8.3
Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.
The contents of this forum are to be used ONLY by readers of the Learning From Data book by Yaser S. Abu-Mostafa, Malik Magdon-Ismail, and Hsuan-Tien Lin, and participants in the Learning From Data MOOC by Yaser S. Abu-Mostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.