Embedding with a Lipschitz function
Copyright policy )Embedding with a Lipschitz function
AbstractWe investigate a new notion of embedding of subsets of {−1,1}n in a given normed space, in a way which preserves the structure of the given set as a class of functions on {1, …, n}. This notion is an extension of the margin parameter often used in Nonparametric Statistics. Our main result is that even when considering “small” subsets of {−1, 1}n, the vast majority of such sets do not embed in a better way than the entire cube in any normed space that satisfies a minor structural assumption. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005
- Australian National University Australia
embedding, local theory of normed spaces, Random Sets, margin, Lipschitz function, Keywords: Embedding with a Lipschitz Function, Probabilistic methods in Banach space theory, Local theory of Banach spaces, Local Theory of Normed Spaces, random sets, Margin
embedding, local theory of normed spaces, Random Sets, margin, Lipschitz function, Keywords: Embedding with a Lipschitz Function, Probabilistic methods in Banach space theory, Local theory of Banach spaces, Local Theory of Normed Spaces, random sets, Margin
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