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Boltzmann machine and mean-field approximation for structured sparse decompositions

Abstract

Taking advantage of the structures inherent in many sparse decompositions constitutes a promising research axis. In this paper, we address this problem from a Bayesian point of view. We exploit a Boltzmann machine, allowing to take a large variety of structures into account, and focus on the resolution of a marginalized maximum a posteriori problem. To solve this problem, we resort to a mean-field approximation and the variational Bayes Expectation-Maximization" algorithm. This approach results in a soft procedure making no hard decision in the support or the values of the sparse representation. We show that this characteristic leads to an improvement of the performance over state-of-the-art algorithms.
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Dates and versions

hal-00648089 , version 1 (05-12-2011)
hal-00648089 , version 2 (16-03-2012)

Identifiers

  • HAL Id : hal-00648089 , version 2

Cite

Angélique Drémeau, Cédric Herzet, Laurent Daudet. Boltzmann machine and mean-field approximation for structured sparse decompositions. 2012. ⟨hal-00648089v2⟩
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