Bayesian hierarchical models and inference for musical audio processing

In music transcription and related musical signal processing applications we are interested in determining the activity of a set of sound-generating sources having extracted features such as DFT coefficients, spectral peaks from the audio, over time. A probabilistic treatment requires the construction of a Bayesian hierarchy: a dynamical model of how the source activity changes over time, and a generative model of how the features are produced from the active sources. The resulting Bayesian network is of extremely large dimension, for which standard MCMC and variational inference methods struggle. In this paper we describe some models developed recently for these tasks, which also have utility in audio and general signal processing applications; and investigate hybrid inference strategies: sequential methods such as particle filtering on the source activity dynamics coupled with MCMC inference over latent parameters on the generative models, demonstrating their performance for real data.