Low-rank matrix denoising for count data using unbiased Kullback-Leibler risk estimation

Jérémie Bigot and Charles Deledalle

Computational Statistics & Data Analysis, 2022, vol. 169, issue C

Abstract: Many statistical studies are concerned with the analysis of observations organized in a matrix form whose elements are count data. When these observations are assumed to follow a Poisson or a multinomial distribution, it is of interest to focus on the estimation of either the intensity matrix (Poisson case) or the compositional matrix (multinomial case) when it is assumed to have a low rank structure. In this setting, it is proposed to construct an estimator minimizing the regularized negative log-likelihood by a nuclear norm penalty. Such an approach easily yields a low-rank matrix-valued estimator with positive entries which belongs to the set of row-stochastic matrices in the multinomial case. Then, as a main contribution, a data-driven procedure is constructed to select the regularization parameter in the construction of such estimators by minimizing (approximately) unbiased estimates of the Kullback-Leibler (KL) risk in such models, which generalize Stein's unbiased risk estimation originally proposed for Gaussian data. The evaluation of these quantities is a delicate problem, and novel methods are introduced to obtain accurate numerical approximation of such unbiased estimates. Simulated data are used to validate this way of selecting regularizing parameters for low-rank matrix estimation from count data. For data following a multinomial distribution, the performances of this approach are also compared to K-fold cross-validation. Examples from a survey study and metagenomics also illustrate the benefits of this methodology for real data analysis.

Keywords: Low-rank matrix denoising; Count data; Poisson distribution; Multinomial distribution; Nuclear norm penalization; Kullback-Leibler risk; Generalized Stein's unbiased risk estimate; Optimal shrinkage rule; Survey study; Metagenomics data (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947322000032
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:169:y:2022:i:c:s0167947322000032

DOI: 10.1016/j.csda.2022.107423

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().