Flexible and Hierarchical Prior for Bayesian Nonnegative Matrix Factorization

TL;DR

This paper presents a Bayesian nonnegative matrix factorization model with hierarchical priors, improving prediction accuracy and overfitting prevention in real-world datasets through Gibbs sampling inference.

Contribution

It introduces a novel hierarchical prior for Bayesian NMF that enhances predictive performance and robustness over existing methods.

Findings

Better prediction accuracy on MovieLens datasets

Reduced overfitting compared to previous Bayesian NMF models

Effective handling of missing data in real-world applications

Abstract

In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent variables associated with each data dimension. The nonnegativity constraint for the latent factors is handled by choosing priors with support on the nonnegative subspace. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including MovieLens 100K and MovieLens 1M with different sizes and dimensions and show that the proposed Bayesian NMF GRRN model leads to better predictions and avoids overfitting compared to existing Bayesian NMF approaches.