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The shattering dimension of sets of linear functionals

Schechtman, Gideon; Mendelson, Shahar

Description

We evaluate the shattering dimension of various classes of linear functionals on various symmetric convex sets. The proofs here relay mostly on methods from the local theory of normed spaces and include volume estimates, factorization techniques and tail estimates of norms, viewed as random variables on Euclidean spheres. The estimates of shattering dimensions can be applied to obtain error bounds for certain classes of functions, a fact which was the original motivation of this study....[Show more]

CollectionsANU Research Publications
Date published: 2004
Type: Journal article
URI: http://hdl.handle.net/1885/100163
Source: The Annals of Probability
DOI: 10.1214/009117904000000388

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