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Embedding with a Lipschitz Function

Mendelson, Shahar

Description

We 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.

CollectionsANU Research Publications
Date published: 2005
Type: Journal article
URI: http://hdl.handle.net/1885/79787
Source: Random Structures and Algorithms
DOI: 10.1002/rsa.20054

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