The shattering dimension of sets of linear functionals

Shahar Mendelson*, Gideon Schechtman

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)

    Abstract

    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. Although this can probably be done in a more traditional manner, we also use the approach presented here to determine whether several classes of linear functionals satisfy the uniform law of large numbers and the uniform central limit theorem.

    Original languageEnglish
    Pages (from-to)1746-1770
    Number of pages25
    JournalAnnals of Probability
    Volume32
    Issue number3 A
    DOIs
    Publication statusPublished - Jul 2004

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