Communications in Mathematical Sciences
Volume 19 (2021)
Hierarchical low-rank structure of parameterized distributions
Pages: 865 – 874
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