A Matrix Expander Chernoff Bound
Probability
2018-04-18 v3 Computational Complexity
Data Structures and Algorithms
Abstract
We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a random walk on an expander, confirming a conjecture due to Wigderson and Xiao. Our proof is based on a new multi-matrix extension of the Golden-Thompson inequality which improves in some ways the inequality of Sutter, Berta, and Tomamichel, and may be of independent interest, as well as an adaptation of an argument for the scalar case due to Healy. Secondarily, we also provide a generic reduction showing that any concentration inequality for vector-valued martingales implies a concentration inequality for the corresponding expander walk, with a weakening of parameters proportional to the squared mixing time.
Cite
@article{arxiv.1704.03864,
title = {A Matrix Expander Chernoff Bound},
author = {Ankit Garg and Yin Tat Lee and Zhao Song and Nikhil Srivastava},
journal= {arXiv preprint arXiv:1704.03864},
year = {2018}
}
Comments
Fixed a minor bug in the proof of Theorem 3.4