Bernstein Concentration Inequalities for Tensors via Einstein Products
arXiv:1902.030569 citationsh-index: 74
AI Analysis
Provides a theoretical tool for analyzing random tensors, which is relevant for machine learning and data analysis applications involving tensor data.
This paper generalizes Bernstein's matrix concentration inequality to tensors of arbitrary order using Einstein products, enabling the derivation of tensor concentration bounds from existing matrix results.
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.