- #1
zzmanzz
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Homework Statement
Linear family:
[tex]f(x;a) = a_{o} + (a_{1}.a_{2},a_{3},...,a_{k}) \cdot x[\tex]
[tex] (Xa - Y)^t \sigma^{-1} (Xa-Y) + \lambda (a^t a-a^2_{o} [\tex]
[tex] a = (X^t \sigma^{-1} X + \lamda I_{o})^{-1} x^t \sigma^{-1} Y [\tex]
Homework Equations
[tex] Y_{i} = f(x_{i}) + N_{i} [\tex]i = 1,2,3,4,...,k.
given data [tex] \{ (x_{i},y_{i})\}^2_{i} [\tex]
[tex] x_{i} [\tex] = vector
[tex] y_{i} [\tex] = scalar
to minimize we write
[tex](X(a+\Delta a) - Y)^t \sigma^{-1} (X(a+\Delta a)-Y)[\tex]
[tex]=(Xa - Y)^t \sigma^{-1} (Xa-Y) + \Delta a^t X^t \sigma^{-1} (Xa-Y)+(Xa-Y)^t \sigma^{-1} + O(\Delta a^t \Delta a)[\tex]
[tex]=(Xa - Y)^t \sigma^{-1} (Xa-Y) + 2\Delta a^t X^t \sigma^{-1} (Xa-Y) + O(\Delta a^t \Delta a)
[\tex]
cond for a:
[tex]X^t \sigma^{-1} Xa - X^t \sigma^{-1} X = 0[\tex]
[tex]a = (X^t \sigma^{-1} X)^(-1)X^t \sigma^{-1} Y[\tex]
The Attempt at a Solution
Sorry can someone tell me why my latex is off? I am new to the forums and did my best to use the code? Thanks, I will repost.
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