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Old 05-14-2013, 07:54 PM
Dorian Dorian is offline
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Default 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.
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Old 05-14-2013, 09:59 PM
Joe Turner Joe Turner is offline
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Default 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?
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Old 05-14-2013, 10:38 PM
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yaser yaser is offline
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Default Re: validation exercises, unclear about non-linear transformation functions

Quote:
Originally Posted by Dorian View Post
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.
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Old 05-16-2013, 03:51 PM
Dorian Dorian is offline
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Default 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.
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Old 05-16-2013, 04:02 PM
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yaser yaser is offline
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Default Re: validation exercises, unclear about non-linear transformation functions

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Originally Posted by Dorian View Post
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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