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Old 10-08-2014, 06:33 PM
squidsforlunch squidsforlunch is offline
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Default 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?
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Old 10-09-2014, 10:53 AM
mddsangster mddsangster is offline
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Join Date: Oct 2014
Posts: 4
Default 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 View Post
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?
Reply With Quote
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