An adaptive Monte-Carlo Markov chain algorithm for inference from mixture signals

R. Bardenet 1, 2 Balázs Kégl 3, 4, 1
1 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
2 Pierre Auger
LAL - Laboratoire de l'Accélérateur Linéaire, LRI - Laboratoire de Recherche en Informatique
Abstract : Adaptive Metropolis (AM) is a powerful recent algorithmic tool in numerical Bayesian data analysis. AM builds on a well-known Markov Chain Monte Carlo algorithm but optimizes the rate of convergence to the target distribution by automatically tuning the design parameters of the algorithm on the fly. Label switching is a major problem in inference on mixture models because of the invariance to symmetries. The simplest (non-adaptive) solution is to modify the prior in order to make it select a single permutation of the variables, introducing an identifiability constraint. This solution is known to cause artificial biases by not respecting the topology of the posterior. In this paper we describe an online relabeling procedure which can be incorporated into the AM algorithm. We give elements of convergence of the algorithm and identify the link between its modified target measure and the original posterior distribution of interest. We illustrate the algorithm on a synthetic mixture model inspired by the muonic water Cherenkov signal of the surface detectors in the Pierre Auger Experiment.
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Conference papers
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Submitted on : Wednesday, July 4, 2012 - 5:12:47 PM
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R. Bardenet, Balázs Kégl. An adaptive Monte-Carlo Markov chain algorithm for inference from mixture signals. 14th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2011), Sep 2011, Uxbridge, United Kingdom. pp.012044, ⟨10.1088/1742-6596/368/1/012044⟩. ⟨in2p3-00714497⟩

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