Majorize-Minimize Adapted Metropolis-Hastings Algorithm

Abstract : The dimension and the complexity of inference problems have dramatically increased in statistical signal processing. It thus becomes mandatory to design improved proposal schemes in Metropolis-Hastings algorithms, providing large proposal transitions that are accepted with high probability. The proposal density should ideally provide an accurate approximation of the target density with a low computational cost. In this paper, we derive a novel Metropolis-Hastings proposal, inspired from Langevin dynamics, where the drift term is preconditioned by an adaptive matrix constructed through a Majorization-Minimization strategy. We propose several variants of low-complexity curvature metrics applicable to large scale problems. We demonstrate the geometric ergodicity of the resulting chain for the class of super-exponential distributions. The proposed method is shown to exhibit a good performance in two signal recovery examples.
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Submitted on : Tuesday, October 30, 2018 - 8:29:00 PM
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  • HAL Id : hal-01909153, version 1

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Yosra Marnissi, Emilie Chouzenoux, Amel Benazza-Benyahia, Jean-Christophe Pesquet. Majorize-Minimize Adapted Metropolis-Hastings Algorithm. 2018. ⟨hal-01909153⟩

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