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

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