  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.
