Tensor Bernstein concentration inequalities with an application to sample estimators for high-order moments

Ziyan Luo, Liqun Qi, Philippe L. Toint

Research output: Contribution to journalArticlepeer-review

Abstract

This paper develops the Bernstein tensor concentration inequality for random tensors of general order, based on the use of Einstein products for tensors. This establishes a strong link between these and matrices, which in turn allows exploitation of existing results for the latter. An interesting application to sample estimators of high-order moments is presented as an illustration.

Original languageEnglish
Pages (from-to)367-384
Number of pages18
JournalFrontiers of Mathematics in China
Volume15
Issue number2
DOIs
Publication statusPublished - 1 Apr 2020
Externally publishedYes

Keywords

  • computational statistics
  • concentration inequality
  • Einstein products
  • Random tensors
  • sub-sampling

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