DeepAI AI Chat
Log In Sign Up

Sparse random tensors: concentration, regularization and applications

by   Zhixin Zhou, et al.

We prove a non-asymptotic concentration inequality of sparse inhomogeneous random tensors under the spectral norm. For an order-k inhomogeneous random tensor T with sparsity p_max≥clog n/n^k-1, we show that T-E T=O(√(np_max)) with high probability. We also provide a simple way to regularize T such that O(√(np_max)) concentration still holds down to sparsity p_max>c/n^k-1. Our proofs are based on the techniques of Friedman, Kahn and Szemerédi (1989), Feige and Ofek (2005), with the discrepancy theory of random hypergraphs. We also show that our concentration inequality is rate optimal in the minimax sense. We present our concentration and regularization results with three applications: (i) a randomized construction of hypergraphs of bounded degrees with good expander mixing properties, (ii) concentration of the adjacency matrices for sparse random hypergraphs, and (iii) concentration of sparsified tensors under uniform sampling.


page 1

page 2

page 3

page 4


Bernstein Concentration Inequalities for Tensors via Einstein Products

A generalization of the Bernstein matrix concentration inequality to ran...

A matrix concentration inequality for products

We present a non-asymptotic concentration inequality for the random matr...

Uniform Hanson-Wright type concentration inequalities for unbounded entries via the entropy method

This paper is devoted to uniform versions of the Hanson-Wright inequalit...

Concentration of Non-Isotropic Random Tensors with Applications to Learning and Empirical Risk Minimization

Dimension is an inherent bottleneck to some modern learning tasks, where...

A Concentration Bound for LSPE(λ)

The popular LSPE(λ) algorithm for policy evaluation is revisited to deri...

Concentration of the Frobenius norms of generalized matrix inverses

In many applications it is useful to replace the Moore-Penrose pseudoinv...

Measure Concentration on the OFDM-based Random Access Channel

It is well known that CS can boost massive random access protocols. Usua...