Inference and learning in gamma chains for Bayesian audio processing
Ali Taylan Cemgil, Onur Dikmen · The Journal of the Acoustical Society of America · 2008
Statistical description of complex phenomena encountered in many applications requires construction of nonstationary models. A first step in analysis of such nonstationary sources involves typically a traditional time-frequency analysis Short time Fourier transform. In all these techniques, the underlying implicit assumption is that the process is piecewise stationarity, however dependencies across frequency bands or time frames are not explicitly characterised. Here, we investigate a class of prior models, called Gamma chains, for modelling such statistical dependencies in the time-frequency representations of signals. In particular, we model the prior variance of transform coefficients using Markov chains, trees and fields of inverse Gamma random variables. This model class is Markovian and conditionally conjugate, so standard inference methods like Gibbs sampling, variational Bayes or sequential Monte Carlo can be applied effectively and efficiently. We also show how hyperparameters, that determine the coupling between prior variances of transform coefficients, can also be optimised. We discuss the pros and cons of various inference schemata (variational Bayes, Gibss sampler and particle filtering) in terms of complexity and optimisation performance for this model class. We illustrate the effectiveness of our approach in audio denoising and single channel audio source separation applications.