Exact Bayesian estimation in constrained Triplet Markov Chains

Yohan Petetin; François Desbouvries

doi:10.1109/MLSP.2014.6958847

Exact Bayesian estimation in constrained Triplet Markov Chains

Yohan Petetin, François Desbouvries

CEA/UVSQ/CNRS

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The Jump Markov state-space system (JMSS) is a well known model for representing dynamical models with jumps. However inference in a JMSS model is NP-hard, even in the conditionally linear and Gaussian case. Suboptimal solutions include Sequential Monte Carlo (SMC) and Interacting Multiple Models (IMM) methods. In this paper, we build a constrained Triplet Markov Chain (TMC) model which is close to the given JMSS model, and in which moments of interest can be computed exactly (without resorting to numerical nor Monte Carlo approximations) and at a computational cost which is linear in the number of observations. Additionnally, a side advantage of our technique is that it can be used easily in a partially known model context.

Original language	English
Title of host publication	IEEE International Workshop on Machine Learning for Signal Processing, MLSP
Editors	Mamadou Mboup, Tulay Adali, Eric Moreau, Jan Larsen
Publisher	IEEE Computer Society
ISBN (Electronic)	9781479936946
DOIs	https://doi.org/10.1109/MLSP.2014.6958847
Publication status	Published - 14 Nov 2014
Event	2014 24th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2014 - Reims, France Duration: 21 Sept 2014 → 24 Sept 2014

Publication series

Name	IEEE International Workshop on Machine Learning for Signal Processing, MLSP
ISSN (Print)	2161-0363
ISSN (Electronic)	2161-0371

Conference

Conference	2014 24th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2014
Country/Territory	France
City	Reims
Period	21/09/14 → 24/09/14

Keywords

Bayesian estimation
Expectation Maximization
Jump Markov state-space systems
Triplet Markov chains

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10.1109/MLSP.2014.6958847

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Petetin, Y., & Desbouvries, F. (2014). Exact Bayesian estimation in constrained Triplet Markov Chains. In M. Mboup, T. Adali, E. Moreau, & J. Larsen (Eds.), IEEE International Workshop on Machine Learning for Signal Processing, MLSP Article 6958847 (IEEE International Workshop on Machine Learning for Signal Processing, MLSP). IEEE Computer Society. https://doi.org/10.1109/MLSP.2014.6958847

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title = "Exact Bayesian estimation in constrained Triplet Markov Chains",

abstract = "The Jump Markov state-space system (JMSS) is a well known model for representing dynamical models with jumps. However inference in a JMSS model is NP-hard, even in the conditionally linear and Gaussian case. Suboptimal solutions include Sequential Monte Carlo (SMC) and Interacting Multiple Models (IMM) methods. In this paper, we build a constrained Triplet Markov Chain (TMC) model which is close to the given JMSS model, and in which moments of interest can be computed exactly (without resorting to numerical nor Monte Carlo approximations) and at a computational cost which is linear in the number of observations. Additionnally, a side advantage of our technique is that it can be used easily in a partially known model context.",

keywords = "Bayesian estimation, Expectation Maximization, Jump Markov state-space systems, Triplet Markov chains",

author = "Yohan Petetin and Fran{\c c}ois Desbouvries",

note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 2014 24th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2014 ; Conference date: 21-09-2014 Through 24-09-2014",

year = "2014",

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doi = "10.1109/MLSP.2014.6958847",

language = "English",

series = "IEEE International Workshop on Machine Learning for Signal Processing, MLSP",

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Petetin, Y & Desbouvries, F 2014, Exact Bayesian estimation in constrained Triplet Markov Chains. in M Mboup, T Adali, E Moreau & J Larsen (eds), IEEE International Workshop on Machine Learning for Signal Processing, MLSP., 6958847, IEEE International Workshop on Machine Learning for Signal Processing, MLSP, IEEE Computer Society, 2014 24th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2014, Reims, France, 21/09/14. https://doi.org/10.1109/MLSP.2014.6958847

Exact Bayesian estimation in constrained Triplet Markov Chains. / Petetin, Yohan ; Desbouvries, François.
IEEE International Workshop on Machine Learning for Signal Processing, MLSP. ed. / Mamadou Mboup; Tulay Adali; Eric Moreau; Jan Larsen. IEEE Computer Society, 2014. 6958847 (IEEE International Workshop on Machine Learning for Signal Processing, MLSP).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Desbouvries, François

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N2 - The Jump Markov state-space system (JMSS) is a well known model for representing dynamical models with jumps. However inference in a JMSS model is NP-hard, even in the conditionally linear and Gaussian case. Suboptimal solutions include Sequential Monte Carlo (SMC) and Interacting Multiple Models (IMM) methods. In this paper, we build a constrained Triplet Markov Chain (TMC) model which is close to the given JMSS model, and in which moments of interest can be computed exactly (without resorting to numerical nor Monte Carlo approximations) and at a computational cost which is linear in the number of observations. Additionnally, a side advantage of our technique is that it can be used easily in a partially known model context.

AB - The Jump Markov state-space system (JMSS) is a well known model for representing dynamical models with jumps. However inference in a JMSS model is NP-hard, even in the conditionally linear and Gaussian case. Suboptimal solutions include Sequential Monte Carlo (SMC) and Interacting Multiple Models (IMM) methods. In this paper, we build a constrained Triplet Markov Chain (TMC) model which is close to the given JMSS model, and in which moments of interest can be computed exactly (without resorting to numerical nor Monte Carlo approximations) and at a computational cost which is linear in the number of observations. Additionnally, a side advantage of our technique is that it can be used easily in a partially known model context.

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KW - Expectation Maximization

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KW - Triplet Markov chains

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M3 - Conference contribution

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BT - IEEE International Workshop on Machine Learning for Signal Processing, MLSP

A2 - Mboup, Mamadou

A2 - Adali, Tulay

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A2 - Larsen, Jan

PB - IEEE Computer Society

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ER -

Exact Bayesian estimation in constrained Triplet Markov Chains

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