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Old 05-18-2013, 02:42 PM
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yaser yaser is offline
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Join Date: Aug 2009
Location: Pasadena, California, USA
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Default Re: Questions 1-4: Clarification

Quote:
Originally Posted by Kekeli View Post
So the models k=3..7 correspond to

\phi_3 = 1 + x_1 + x_2 + x_1^2

\phi_4 = 1 + x_1 + x_2 + x_1^2 + x_2^2
etc.?
The transformed space in the case of k=3 would be

{\bf z}=(\phi_0({\bf x}),\phi_1({\bf x}),\phi_2({\bf x}),\phi_3({\bf x}))=(1,x_1,x_2,x_1^2)

The model (hypothesis set) would be a linear combination of these coordinates,

h({\bf x})=\tilde{w}_0 \phi_0({\bf x})+\tilde{w}_1 \phi_1({\bf x})+\tilde{w}_2\phi_2({\bf x})+\tilde{w}_3\phi_3({\bf x})
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