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

Understand

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.