Communications in Mathematical Sciences

Volume 19 (2021)

Number 3

Hierarchical low-rank structure of parameterized distributions

Pages: 865 – 874

(Fast Communication)



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

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


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.


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

2010 Mathematics Subject Classification

41A35, 62E17, 62H10, 94A15

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