Embedding with a Lipschitz Function

Abstract

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. Show more