LFD Book Forum

LFD Book Forum (http://book.caltech.edu/bookforum/index.php)
-   Chapter 3 - The Linear Model (http://book.caltech.edu/bookforum/forumdisplay.php?f=110)
-   -   Exercise 3.4(a) (http://book.caltech.edu/bookforum/showthread.php?t=4512)

squidsforlunch 10-08-2014 05:33 PM

Exercise 3.4(a)
 
For Exercise 3.4 (a) I did

y = w*^{T}X+E
\hat{y} = Hy
\hat{y} = H(w*^{T}X+E)
\hat{y} = Hw*^{T}x+HE
\hat{y} = (X(X^{T}X)^{-1}X^{T})w*^{T}X+HE
\hat{y} = (XX^{-1}(X^{T})^{-1}X^{T})w*^{T}X+HE
\hat{y} = (I(X^{T})^{-1}X^{T})w*^{T}X+HE
\hat{y} = (I(I))w*^{T}X+HE
\hat{y} = w*^{T}X+HE

but
w*^{T}X
is not equal to
Xw*
What am I missing?

mddsangster 10-09-2014 09:53 AM

Re: Exercise 3.4(a)
 
Everything is right, however;
y = w*^{T}X+E

the signal
y_n = w*^{T} x_n+ \epsilon
over the entire domain of x becomes

y = Xw^* +  \epsilon

from pg 84 :
the nth component of the vector Xw-y is exactly w^{T}x_n-y_n


Quote:

Originally Posted by squidsforlunch (Post 11761)
For Exercise 3.4 (a) I did

y = w*^{T}X+E
\hat{y} = Hy
\hat{y} = H(w*^{T}X+E)
\hat{y} = Hw*^{T}x+HE
\hat{y} = (X(X^{T}X)^{-1}X^{T})w*^{T}X+HE
\hat{y} = (XX^{-1}(X^{T})^{-1}X^{T})w*^{T}X+HE
\hat{y} = (I(X^{T})^{-1}X^{T})w*^{T}X+HE
\hat{y} = (I(I))w*^{T}X+HE
\hat{y} = w*^{T}X+HE

but
w*^{T}X
is not equal to
Xw*
What am I missing?



All times are GMT -7. The time now is 10:41 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.