Empirical processes and random projections

B. Klartag*, Shabar Mendelson

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    55 Citations (Scopus)

    Abstract

    In this note, we establish some bounds on the supremum of certain empirical processes indexed by sets of functions with the same L2 norm. We present several geometric applications of this result, the most important of which is a sharpening of the Johnson-Lindenstrauss embedding Lemma. Our results apply to a large class of random matrices, as we only require that the matrix entries have a subgaussian tail.

    Original languageEnglish
    Pages (from-to)229-245
    Number of pages17
    JournalJournal of Functional Analysis
    Volume225
    Issue number1
    DOIs
    Publication statusPublished - 1 Aug 2005

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