Talk:Vapnik–Chervonenkis theory
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The concept
[edit]The concept of "shatter" or "shattering" is vitally important in the fields of statistical learning theory, empirical processes, and probability theory in general. I have begun to improve the article entitled "shatter", but although it needs more content, it does indeed warrent an article of its own. Moreover, soon, I hope to begin an article on empirical processes, which is not in the Wikepedia yet, but really warrents an entry. I appreciate the editing and improvements made by Trovatore to my new article on shattering (which made many needed corrections to the earlier article, which was a good start, but had some difficulties about sets, subsets, and classes of sets) which I will continue to augment. -- sorry I am new at Wikipedia, but an old time mathematician. Sorry; forgot to sign in this time...will try to remember next time. Thanks again, Trovatore. Would like to discuss more about how we needed to invoke the Axiom of Choice in some of our work on shattering, and did indeed run into Russell's paradox.
I moved the article on statistical learning theory over to here, because "VC theory" is how a large majority of learning theorists refer to Vapnik's work. Otherwise, there is too much confusion between this theory and the general field of computational learning theory.
This is also known as VC theory. -- hike395 22:18, 9 Oct 2004 (UTC)
The definition in shatter is not in general use in set theory, and is kind of a trivial dicdef standing on its own. Maybe someone could give it some context and a home in this article. --Trovatore 05:07, 5 October 2005 (UTC)
- Actually it looks like it should be merged into VC dimension instead. --Trovatore 06:04, 5 October 2005 (UTC)
Vapnik Chervonenkis theory and empirical processes
[edit]VC-theory, with a somewhat different approach, is important in the field of empirical processes. As the article on empirical processes is expanded, this will become apparent. Is it all right with everyone out there to add the empirical-process approach to VC-theory within this article? MathStatWoman 17:54, 20 January 2006 (UTC)
Expansion of this intro to VC Theory
[edit]Hi I have made an extension of this article which can be seen on my sandbox. It is a self-contained intro to VC theory in Empirical Processes and VC inequality. I have removed the algorithm parts because VC theory can be applied to show generalization for SVM for example, but it doesn't really has to do with introducing the algorithmic part of SVM. I also made some connections with symmetrization, which is a technique widely used in the proofs of stuff like VC inequality and in empirical processes. Any comments and suggestions would be appreciated, and I am ultimately interested in uploading this expansion so every opinion/suggestion would be appreciated.
Problem Found
[edit]In the VC connection section is says that 2v/(v+2)>2, but this is true for no v. Also the article uses K and v without defining it — Preceding unsigned comment added by 68.198.148.137 (talk) 16:03, 30 September 2016 (UTC)