Relabeling and Summarizing Posterior Distributions in Signal Decomposition Problems When the Number of Components is Unknown
| العنوان: | Relabeling and Summarizing Posterior Distributions in Signal Decomposition Problems When the Number of Components is Unknown |
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| المؤلفون: | Julien Bect, Alireza Roodaki, Gilles Fleury |
| المساهمون: | Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Supélec Sciences des Systèmes (E3S), Ecole Supérieure d'Electricité - SUPELEC (FRANCE) |
| المصدر: | IEEE Transactions on Signal Processing IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2014, 62 (16), pp.4091-4104. ⟨10.1109/TSP.2014.2333569⟩ |
| بيانات النشر: | Institute of Electrical and Electronics Engineers (IEEE), 2014. |
| سنة النشر: | 2014 |
| مصطلحات موضوعية: | FOS: Computer and information sciences, Mathematical optimization, Signal decomposition, Stochastic EM, Bayesian inference, Monte Carlo method, Posterior probability, 02 engineering and technology, Statistics - Computation, 01 natural sciences, 010104 statistics & probability, symbols.namesake, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Electrical and Electronic Engineering, [STAT.CO]Statistics [stat]/Computation [stat.CO], Divergence (statistics), Computation (stat.CO), Mathematics, Variable (mathematics), Label-switching, 020206 networking & telecommunications, Trans-dimensional MCMC, Statistics::Computation, Additive white Gaussian noise, Counting problem, Signal Processing, symbols, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Algorithm, Curse of dimensionality |
| الوصف: | This paper addresses the problems of relabeling and summarizing posterior distributions that typically arise, in a Bayesian framework, when dealing with signal decomposition problems with an unknown number of components. Such posterior distributions are defined over union of subspaces of differing dimensionality and can be sampled from using modern Monte Carlo techniques, for instance the increasingly popular RJ-MCMC method. No generic approach is available, however, to summarize the resulting variable-dimensional samples and extract from them component-specific parameters. We propose a novel approach, named Variable-dimensional Approximate Posterior for Relabeling and Summarizing (VAPoRS), to this problem, which consists in approximating the posterior distribution of interest by a "simple"---but still variable-dimensional---parametric distribution. The distance between the two distributions is measured using the Kullback-Leibler divergence, and a Stochastic EM-type algorithm, driven by the RJ-MCMC sampler, is proposed to estimate the parameters. Two signal decomposition problems are considered, to show the capability of VAPoRS both for relabeling and for summarizing variable dimensional posterior distributions: the classical problem of detecting and estimating sinusoids in white Gaussian noise on the one hand, and a particle counting problem motivated by the Pierre Auger project in astrophysics on the other hand. arXiv admin note: text overlap with arXiv:1111.6298 |
| تدمد: | 1941-0476 1053-587X |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3152799856d286c081b5d17fa6ee8055 https://doi.org/10.1109/tsp.2014.2333569 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....3152799856d286c081b5d17fa6ee8055 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 19410476 1053587X |
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