Probabilistic Modelling of Signal Mixtures with Differentiable Dictionaries

TL;DR

This paper presents a new probabilistic approach called differentiable dictionary search for modeling complex signal mixtures, enhancing non-negative matrix factorization with prior information, and demonstrates its effectiveness on audio decomposition tasks.

Contribution

It introduces a novel differentiable dictionary search method that integrates prior knowledge into semi-supervised non-negative matrix factorization for better modeling of non-linear source mixtures.

Findings

Effective in audio decomposition tasks

Flexible and principled modeling of mixtures

Extensive controlled study of capabilities

Abstract

We introduce a novel way to incorporate prior information into (semi-) supervised non-negative matrix factorization, which we call differentiable dictionary search. It enables general, highly flexible and principled modelling of mixtures where non-linear sources are linearly mixed. We study its behavior on an audio decomposition task, and conduct an extensive, highly controlled study of its modelling capabilities.