Biwhitening Reveals the Rank of a Count Matrix

ABSTRACT: Estimating the rank of a corrupted data matrix is an important task in data analysis, most notably for choosing the number of components in PCA. Significant progress on this task was achieved using random matrix theory by characterizing the spectral properties of large noise matrices. However, utilizing such tools is not straightforward when the data matrix consists of count random variables, e.g., Poisson, in which case the noise can be heteroskedastic with an unknown variance in each entry. In this work, we focus on a Poisson random matrix with independent entries and propose a simple procedure, termed biwhitening, for estimating the rank of the underlying signal matrix (i.e., the Poisson parameter matrix) without any prior knowledge. Our approach is based on the key observation that one

SUBMITTER: Landa B 

PROVIDER: S-EPMC10417917 | biostudies-literature | 2022 Jan

REPOSITORIES: biostudies-literature