Robust Bayesian Nonnegative Matrix Factorization with Implicit Regularizers

TL;DR

This paper presents a robust Bayesian nonnegative matrix factorization model with implicit regularizers, improving prediction accuracy and overfitting resistance on real-world datasets through a probabilistic approach with Gibbs sampling.

Contribution

It introduces a novel Bayesian NMF model with implicit norm regularization and demonstrates its effectiveness on various real-world datasets.

Findings

Enhanced prediction robustness across datasets

Reduced overfitting compared to existing Bayesian NMF methods

Effective handling of missing data in NMF applications

Abstract

We introduce a probabilistic model with implicit norm regularization 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, e.g., exponential density or distribution based on exponential function. Bayesian inference procedure based on Gibbs sampling is employed. We evaluate the model on several real-world datasets including Genomics of Drug Sensitivity in Cancer (GDSC $IC_{50}$) and Gene body methylation with different sizes and dimensions, and show that the proposed Bayesian NMF GL$_2^2$ and GL$_\infty$ models lead to robust predictions for different data values and avoid overfitting compared with competitive Bayesian NMF approaches.