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The past decade has seen substantial work on the use of non-negative matrixfactorization and its probabilistic counterparts for audio source separation.Although able to capture audio spectral structure well, these models neglectthe non-stationarity and temporal dynamics that are important properties ofaudio. The recently proposed non-negative factorial hidden Markov model(N-FHMM) introduces a temporal dimension and improves source separationperformance. However, the factorial nature of this model makes the complexityof inference exponential in the number of sound sources. Here, we present aBayesian variant of the N-FHMM suited to an efficient variational inferencealgorithm, whose complexity is linear in the number of sound sources. Ouralgorithm performs comparably to exact inference in the original N-FHMM but issignificantly faster. In typical configurations of the N-FHMM, our methodachieves around a 30x increase in speed.

Variational Inference in Non-negative Factorial Hidden Markov Models for Efficient Audio Source Separation