Empirical processes and random projections

B. Klartag; Shabar Mendelson

doi:10.1016/j.jfa.2004.10.009

Empirical processes and random projections

B. Klartag^*, Shabar Mendelson

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

57 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 language	English
Pages (from-to)	229-245
Number of pages	17
Journal	Journal of Functional Analysis
Volume	225
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2004.10.009
Publication status	Published - 1 Aug 2005

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AB - 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.

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KW - Random projections

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Empirical processes and random projections

Abstract

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