Online Bayesian group sparse parameter estimation using a generalized inverse Gaussian Markov chain

In this paper we develop a variational Bayes algorithm for the adaptive estimation of time-varying, group sparse signals. First, we propose a hierarchical Bayesian model that captures the sparsity structure of the signal. Sparsity is imposed by a multivariate Laplace distribution, which is known to be the Bayesian analogue of the adaptive lasso. Sparsity structure is then expressed via a novel generalized inverse Gaussian Markov chain, defined on the parameters of the Laplace distribution. The conjugacy of the model´s prior distributions permits the development of an efficient online variational Bayes algorithm that performs inference on the model parameters. Experimental results verify that capturing sparsity structure leads to improvements on estimation performance.