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 udaykamath 03-27-2013 02:12 PM

Proof of Growth Function when Points are not binary

Prof Dr Yaser
I understand the step by step process in bounding the growth function B(N,k) in terms of recursion using x1,x2...xN data points using structural arrangements. I however started thinking, in a numerical data where x1,x2...xN is real numbers we cannot use this alpha + 2* Beta trick and use the polynomial bound by combination? What is the bounds when data is not binary ? Is it still Polynomial in N, and how?
Thanks

Uday Kamath
PhD candidate
GMU

 yaser 04-08-2013 12:43 PM

Re: Proof of Growth Function when Points are not binary

Quote:
 Originally Posted by udaykamath (Post 10084) I understand the step by step process in bounding the growth function B(N,k) in terms of recursion using x1,x2...xN data points using structural arrangements. I however started thinking, in a numerical data where x1,x2...xN is real numbers we cannot use this alpha + 2* Beta trick and use the polynomial bound by combination? What is the bounds when data is not binary ? Is it still Polynomial in N, and how?
You are correct. For non-binary functions, the argument is more elaborate. This is addressed in Vapnik's book "Statistical Learning Theory" in much detail, and also appears in other books and papers.

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