Communications in Mathematical Sciences

Volume 19 (2021)

Number 3

Hierarchical low-rank structure of parameterized distributions

Pages: 865 – 874

(Fast Communication)

DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n3.a14

Authors

Jun Qin (Target Corporation, Sunnyvale, California, U.S.A.)

Lexing Ying (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)

Abstract

This note shows that the matrix forms of several one-parameter distribution families satisfy a hierarchical low-rank structure. Such families of distributions include binomial, Poisson, and $\chi^2$ distributions. The proof is based on a uniform relative bound of a related divergence function. Numerical results are provided to confirm the theoretical findings.

Keywords

hierarchical low-rankness, parameterized distributions, Kullback–Leibler (KL) divergence

2010 Mathematics Subject Classification

41A35, 62E17, 62H10, 94A15

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The work of L.Y. is partially supported by the U.S. Department of Energy, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program; and by the National Science Foundation under award DMS-1818449.

Received 29 November 2019

Accepted 13 December 2020

Published 5 May 2021