An Oracle Inequality for Quasi-Bayesian Non-Negative Matrix Factorization

TL;DR

This paper establishes an oracle inequality for quasi-Bayesian non-negative matrix factorization, providing theoretical insights into how prior choices influence convergence rates in aggregation methods.

Contribution

It introduces a general oracle inequality for quasi-Bayesian NMF, highlighting the impact of prior distributions on convergence behavior.

Findings

Oracle inequality derived for quasi-Bayesian NMF

Shows prior distribution affects convergence rate

Applicable to a broad class of priors

Abstract

The aim of this paper is to provide some theoretical understanding of quasi-Bayesian aggregation methods non-negative matrix factorization. We derive an oracle inequality for an aggregated estimator. This result holds for a very general class of prior distributions and shows how the prior affects the rate of convergence.