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monkaez
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Homework Statement
f(x;a) = x_o + (a_1,a_2,a_3,...a_d)*x
min a (Xa - Y)^t o^(-1) (Xa - Y)
a = (a_0 a_1 a_2 a_3 a_4 . . . a_d)^t
Homework Equations
Y = (y_1 y_2 y_ 3 ... y_k)
X = Dsign Matrix
The Attempt at a Solution
to minimize write
(X(a+ (delta a) - Y )^t o^(-1) (X (a+ delta a) - Y)
= (Xa - Y)^t o^(-1) (Xa - Y) + (delta a)^t X^t o^(-1) (Xa - Y) + (Xa -Y)^t o^(-1) X (delta a) + O((delta a)^t * (delta a))
= (Xa - Y)^t o^(-1) (Xa - Y) + 2*(delta a)^t X^t o^(-1) (Xa - Y) + + O((delta a)^t * (delta a))
a = (X^t o^(-1) X)^(-1) X^t o^(-1) YThis is directly out of my professors notes and I have no clue how this proves that the resulting product is always the minimum this way?
The above solution a is just the solution for standard least squares problem if o = o^2 * I
a = (X^t X)^(-1)*X^t*Y
I guess my main issue is understanding how the minimization process works and how he drops the terms in the O notation. Any input is greatly appreciated. (I tried using latex but the code doesn't manifest for me and I need to read more about it.)
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