Negative Binomial Matrix Completion

TL;DR

This paper introduces a negative binomial matrix completion model that better handles overdispersed count data than previous Poisson-based methods, using nuclear-norm regularization and proximal gradient descent.

Contribution

It extends matrix completion to overdispersed count data by proposing a negative binomial model with nuclear-norm regularization, solved efficiently via proximal gradient descent.

Findings

NB model outperforms Poisson matrix completion on real data.

The proposed method effectively handles various noise and missing data scenarios.

The model demonstrates superior recovery accuracy in experiments.

Abstract

Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for count data with noise that follows a Poisson distribution, which assumes that the mean and variance are equal. Since overdispersed count data, whose variance is greater than the mean, is more likely to occur in realistic settings, we assume that the noise follows the negative binomial (NB) distribution, which can be more general than the Poisson distribution. In this paper, we introduce NB matrix completion by proposing a nuclear-norm regularized model that can be solved by proximal gradient descent. In our experiments, we demonstrate that the NB model outperforms Poisson matrix completion in various noise and missing data settings on real data.