LFD Book Forum Homework#6 Q2
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#1
05-15-2012, 01:24 AM
 gaurav.jain@umassmed.edu Junior Member Join Date: Apr 2012 Location: Worcester, MA Posts: 3
Homework#6 Q2

hi everyone,
Can anyone please explain me how to transform the data using the nonlinear transformation is given by
phi(x1, x2) = (1, x1, x2, x21, x22 , x1x2, |x1 − x2|, |x1 + x2|)

I am just confused how to use that in my code. I mean for the new values which function to use for transformation?

is it x1=x1^2 and x2=x^2 and so on or something else. I am sure i am missing a big concept here. Any help would be great.

Thanks in advance.
#2
05-15-2012, 08:15 PM
 sakumar Member Join Date: Apr 2012 Posts: 40
Re: Homework#6 Q2

Quote:
 Originally Posted by gaurav.jain@umassmed.edu hi everyone, Can anyone please explain me how to transform the data using the nonlinear transformation is given by phi(x1, x2) = (1, x1, x2, x21, x22 , x1x2, |x1 − x2|, |x1 + x2|) I am just confused how to use that in my code. I mean for the new values which function to use for transformation? is it x1=x1^2 and x2=x^2 and so on or something else. I am sure i am missing a big concept here. Any help would be great. Thanks in advance.
There is a typo in the way you have written the vector above. The 4th term is x1^2, the fifth term is x2^2.

But basically you have the right idea. You are given a data vector with two values. Create a larger data vector of 8 terms, seven of which are dependent on the original two values you are given.

In the new vector the first three terms are 1, x1, x2. The remaining 5 terms are obtained by applying "transformations" to x1 and x2. For example, the sixth term is x1*x2.

Then you do linear regression on the new x matrix you have built which is (for the given in.data) an 8x35 matrix. 35 data vectors, each with 8 terms as above.
#3
05-21-2012, 09:35 PM
 gaurav.jain@umassmed.edu Junior Member Join Date: Apr 2012 Location: Worcester, MA Posts: 3
Re: Homework#6 Q2

Thank you so much. This was very clear. I got the right answers.
#4
05-23-2012, 08:22 AM
 lucifirm Member Join Date: Apr 2012 Posts: 20
Re: Homework#6 Q2

I have a question on the Eout. Should we create a new z or should we use the given test set to compute Eout?

In time, I have used the formula:

E_In_Sample = sum (sign (z*w)~= y)) / N

is this ok for Eout too?
#5
05-23-2012, 09:10 AM
 kkkkk Invited Guest Join Date: Mar 2012 Posts: 71
Re: Homework#6 Q2

Quote:
 Originally Posted by lucifirm I have a question on the Eout. Should we create a new z or should we use the given test set to compute Eout? In time, I have used the formula: E_In_Sample = sum (sign (z*w)~= y)) / N is this ok for Eout too?
If I am reading my code correctly, Eout is calculated from out.dta which is the test set. You cant generate new x or z since you do not know the target fn f.
The formula for Ein and Eout has to be the same so that we can compare them, only the set of test points - in or out of sample, differs.
#6
05-23-2012, 09:44 AM
 lucifirm Member Join Date: Apr 2012 Posts: 20
Re: Homework#6 Q2

Thanks kkkkk.
I did both cases, either generate new points and also used out.dta (no together, just for for comparison) and I'm using the same formula for E_in and E_out. My E_in is approx. 0.03, but I just can't get E_out to go near 0.08.... I'll check the code again, but it doesn't make sense, it's such a simple formula...

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