Uniform Convergence (Combinatorics)
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. For a class of predicates H,! defined on a set X,! and a set of samples x=(x{1},x{2},dots,x{m}),!, where x{i}in X,!, the empirical frequency of hin H,! on x,! is widehat{Q{x}}(h)=frac{1}{m} {i:1leq ileq m,h(x{i})=1} ,!. The Uniform Convergence Theorem states, roughly,that if H,! is "simple" and we draw samples independently (with replacement) from X,! according to a distribution P,!, then with high probability all the empirical frequency will be close to its expectation, where the expectation is given by Q_{P}(h)=P{yin X:h(y)=1},!. Here "simple" means that the Vapnik-Chernovenkis dimension of the class H,! is small relative to the size of the sample.In other words, a sufficiently simple collection of functions behaves roughly the same on a small random sample as it does on the distribution as a whole.
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GarantieWeitere Informationen
- Allgemeine Informationen
- GTIN 09786131374685
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131374685
- Titel Uniform Convergence (Combinatorics)
- Herausgeber Betascript Publishing
- Anzahl Seiten 80
- Genre Mathematik
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