Paper No: 117
Conjugate Gamma Markov random fields for modelling nonstationary sources
Author(s): A. Taylan Cemgil, Onur Dikmen
Abstract
In modelling nonstationary sources, one possible strategy is to define
a latent process of strictly positive variables to model variations in
second order statistics of the underlying process. This can be achieved,
for example, by passing a Gaussian process through a positive
nonlinearity or defining a discrete state Markov chain where each
state encodes a certain regime. However, models with such constructs
turn out to be either not very flexible or non-conjugate, making
inference somewhat harder. In this paper, we introduce a conjugate
(inverse-) gamma Markov Random field model that allows random
fluctuations on variances which are useful as priors for nonstationary
time-frequency energy distributions. The main idea is to introduce
auxiliary variables such that full conditional distributions and
sufficient statistics are readily available as closed form
expressions. This allows straightforward implementation of a Gibbs
sampler or a variational algorithm. We illustrate our approach on
denoising and single channel source separation. |
