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-   -   validation exercises, unclear about non-linear transformation functions (http://book.caltech.edu/bookforum/showthread.php?t=4287)

Dorian 05-14-2013 08:54 PM

validation exercises, unclear about non-linear transformation functions
 
Hi,

I am not completely sure about the definition of the functions \phi_0 to \phi_7 for the validation exercises 1-5.

Is it that \phi_0 is 1+x_1, then the rest keep adding the features until \phi_7 has all of them?

thanks,
Dorian.

Joe Turner 05-14-2013 10:59 PM

Re: validation exercises, unclear about non-linear transformation functions
 
Same question here. Do we have:
\phi_0(x)=1,\phi_1(x)=(1,x_1),\phi_2(x)=(1,x_1,x_2)\ldots, or \phi_0(x)=1,\phi_1(x)=x_1,\phi_2(x)=x_2\ldots?

yaser 05-14-2013 11:38 PM

Re: validation exercises, unclear about non-linear transformation functions
 
Quote:

Originally Posted by Dorian (Post 10839)
Hi,

I am not completely sure about the definition of the functions \phi_0 to \phi_7 for the validation exercises 1-5.

Is it that \phi_0 is 1+x_1, then the rest keep adding the features until \phi_7 has all of them?

thanks,
Dorian.

\phi_0 through \phi_7 correspond to the coordinates given in the preamble to Problem 1, namely 1,x_1, \cdots, |x_1+x_2|. The full transformation of \phi_0 through \phi_k for a given values of k would be given by the vector \phi_0,\phi_1,\cdots,\phi_k.

Dorian 05-16-2013 04:51 PM

Re: validation exercises, unclear about non-linear transformation functions
 
Thanks professor! It had to be a vector, of course.

As in other exercises, coding concrete examples is great and is really the only way to concretely understand what is taught in class.

In this case, are you also trying to illustrate the balance when chosing the size of the validation sample, i.e. we can get closer to Eout chosing a larger sample but Eout itself will get worse, because we are removing too many points from the training set? I try to understand the point of each exercise, I hope I am not making too much of it :)

thanks again,
Dorian.

yaser 05-16-2013 05:02 PM

Re: validation exercises, unclear about non-linear transformation functions
 
Quote:

Originally Posted by Dorian (Post 10852)
are you also trying to illustrate the balance when chosing the size of the validation sample, i.e. we can get closer to Eout chosing a larger sample but Eout itself will get worse, because we are removing too many points from the training set? I try to understand the point of each exercise, I hope I am not making too much of it :)

Indeed, this is one of the issues that the problem tests.


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