Publication Date

6-1-2022

Document Type

Article

Publication Title

Taiwanese Journal of Mathematics

Volume

26

Issue

3

DOI

10.11650/tjm/211201

First Page

571

Last Page

606

Abstract

This work prepares new probability bounds for sums of random, inde-pendent, Hermitian tensors. These probability bounds characterize large-deviation behavior of the extreme eigenvalue of the sums of random tensors. We extend Laplace transform method and Lieb’s concavity theorem from matrices to tensors, and apply these tools to generalize the classical bounds associated with the names Chernoff, Ben-nett, and Bernstein from the scalar to the tensor setting. Tail bounds for the norm of a sum of random rectangular tensors are also derived from corollaries of random Hermitian tensors cases. The proof mechanism can also be applied to tensor-valued martingales and tensor-based Azuma, Hoeffding and McDiarmid inequalities are es-tablished.

Keywords

concentration inequality, Einstein products, random tensors

Comments

This is the Version of Record and can also be read online here.

Department

Applied Data Science

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