Negative Binomial Matrix Factorization for Recommender Systems

TL;DR

This paper introduces Negative Binomial Matrix Factorization (NBMF), a new technique for analyzing over-dispersed count data in recommender systems, improving prediction accuracy over Poisson matrix factorization.

Contribution

The paper presents NBMF, a novel matrix factorization method that models dispersion explicitly, allowing for better handling of count data without pre-processing, and provides two estimation approaches.

Findings

NBMF outperforms Poisson matrix factorization in prediction accuracy.

It effectively models over-dispersed count data.

The method reduces the need for data pre-processing.

Abstract

We introduce negative binomial matrix factorization (NBMF), a matrix factorization technique specially designed for analyzing over-dispersed count data. It can be viewed as an extension of Poisson matrix factorization (PF) perturbed by a multiplicative term which models exposure. This term brings a degree of freedom for controlling the dispersion, making NBMF more robust to outliers. We show that NBMF allows to skip traditional pre-processing stages, such as binarization, which lead to loss of information. Two estimation approaches are presented: maximum likelihood and variational Bayes inference. We test our model with a recommendation task and show its ability to predict user tastes with better precision than PF.