Variational Bayesian approximation with scale mixture prior: a comparison between three algorithms

Abstract : Our aim is to solve a linear inverse problem using various methods based on the Variational Bayesian Approximation (VBA). We choose to take sparsity into account via a scale mixture prior, more precisely a student-t model. The joint posterior of the unknown and hidden variable of the mixtures is approximated via the VBA. To do this approximation, classically the alternate algorithm is used. But this method is not the most efficient. Recently other optimization algorithms have been proposed; indeed classical iterative algorithms of optimization such as the steepest descent method and the conjugate gradient have been studied in the space of the probability densities involved in the Bayesian methodology to treat this problem. The main object of this work is to present these three algorithms and a numerical comparison of their performances.
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Leila Gharsalli, Mohammad-Djafari Ali, Aurélia Fraysse, Thomas Rodet. Variational Bayesian approximation with scale mixture prior: a comparison between three algorithms. 32nd International Workshop on Bayesian Inference and Maximun Entropy Methods in Sciences and Engineerin, Jul 2012, Garching near Munich, Germany. pp.130-138. ⟨hal-00854783⟩

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