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A hamiltonian Monte Carlo method for non-smooth energy sampling

Chaari, Lotfi and Tourneret, Jean-Yves and Chaux, Caroline and Batatia, Hadj A hamiltonian Monte Carlo method for non-smooth energy sampling. (2016) IEEE Transactions on Signal Processing, 64 (21). 5585-5594. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TSP.2016.2585120

Abstract

Efficient sampling from high-dimensional distribu- tions is a challenging issue that is encountered in many large data recovery problems. In this context, sampling using Hamil- tonian dynamics is one of the recent techniques that have been proposed to exploit the target distribution geometry. Such schemes have clearly been shown to be efficient for multidimensional sam- pling but, rather, are adapted to distributions from the exponential family with smooth energy functions. In this paper, we address the problem of using Hamiltonian dynamics to sample from probabil- ity distributions having non-differentiable energy functions such as those based on the l1 norm. Such distributions are being used intensively in sparse signal and image recovery applications. The technique studied in this paper uses a modified leapfrog transform involving a proximal step. The resulting nonsmooth Hamiltonian Monte Carlo method is tested and validated on a number of exper- iments. Results show its ability to accurately sample according to various multivariate target distributions. The proposed technique is illustrated on synthetic examples and is applied to an image denoising problem.

Item Type:Article
Additional Information:Thanks to IEEE editor. The definitive version is avaible at http://ieeexplore.ieee.org. The original PDF of the article can be found at http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7500145
HAL Id:hal-01376544
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Aix-Marseille Université - AMU (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Ecole Centrale Marseille (FRANCE)
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Deposited By: Jean-yves TOURNERET
Deposited On:05 Oct 2016 08:07

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