Empirical processes and random projections

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• 作者：Klartag ; B. ; Mendelson ; S.
• 关键词：Random projections ; Generic chaining ; Empirical processes
• 刊名：Journal of Functional Analysis
• 出版年：2005
• 出版时间：August 1, 2005
• 年：2005
• 卷：225
• 期：1
• 页码：229-245
• 全文大小：259 K

文摘

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.