Bernstein Concentration Inequalities for Tensors via Einstein Products

Abstract

A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established between matrices and tensors, in turn allowing exploitation of existing results for the former.

12 pages

References in corpus (3)

• Newton-Type Methods for Non-Convex Optimization Under Inexact Hessian Information
• Second-Order Optimization for Non-Convex Machine Learning: An Empirical Study
• Adaptive Regularization Algorithms with Inexact Evaluations for Nonconvex Optimization

Cited by in corpus (2)

• Adaptive Regularization Algorithms with Inexact Evaluations for Nonconvex Optimization
• T-Jordan Canonical Form and T-Drazin Inverse based on the T-Product