2018
Míguez, Joaquín; Mariño, Inés P.; Vázquez, Manuel A
Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models Artículo de revista
En: Signal Processing, vol. 142, pp. 281-291, 2018, ISSN: 0165-1684.
Resumen | Enlaces | BibTeX | Etiquetas: Adaptive importance sampling, Bayesian inference, Importance sampling, Parameter estimation, population Monte Carlo, State space models
@article{MIGUEZ2018281,
title = {Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models},
author = {Joaqu\'{i}n M\'{i}guez and In\'{e}s P. Mari\~{n}o and Manuel A V\'{a}zquez},
url = {https://www.sciencedirect.com/science/article/pii/S0165168417302761},
doi = {https://doi.org/10.1016/j.sigpro.2017.07.030},
issn = {0165-1684},
year = {2018},
date = {2018-01-01},
urldate = {2018-01-01},
journal = {Signal Processing},
volume = {142},
pages = {281-291},
abstract = {The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M−12. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.},
keywords = {Adaptive importance sampling, Bayesian inference, Importance sampling, Parameter estimation, population Monte Carlo, State space models},
pubstate = {published},
tppubtype = {article}
}
The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M−12. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.
Míguez, Joaquín; Mariño, Inés P.; Vázquez, Manuel A
Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models Artículo de revista
En: Signal Processing, vol. 142, pp. 281-291, 2018, ISSN: 0165-1684.
Resumen | Enlaces | BibTeX | Etiquetas: Adaptive importance sampling, Bayesian inference, Importance sampling, Parameter estimation, population Monte Carlo, State space models
@article{MIGUEZ2018281b,
title = {Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models},
author = {Joaqu\'{i}n M\'{i}guez and In\'{e}s P. Mari\~{n}o and Manuel A V\'{a}zquez},
url = {https://www.sciencedirect.com/science/article/pii/S0165168417302761},
doi = {https://doi.org/10.1016/j.sigpro.2017.07.030},
issn = {0165-1684},
year = {2018},
date = {2018-01-01},
urldate = {2018-01-01},
journal = {Signal Processing},
volume = {142},
pages = {281-291},
abstract = {The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M−12. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.},
keywords = {Adaptive importance sampling, Bayesian inference, Importance sampling, Parameter estimation, population Monte Carlo, State space models},
pubstate = {published},
tppubtype = {article}
}
The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M−12. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.
2016
Koblents, Eugenia; Míguez, Joaquín; Rodríguez, Marco A; Schmidt, Alexandra M
A Nonlinear Population Monte Carlo Scheme for the Bayesian Estimation of Parameters of α-stable Distributions Artículo de revista
En: Computational Statistics & Data Analysis, vol. 95, pp. 57–74, 2016, ISSN: 01679473.
Resumen | Enlaces | BibTeX | Etiquetas: Animal movement, Bayesian inference, Importance sampling, L{é}vy process, α-stable distributions
@article{Koblents2016,
title = {A Nonlinear Population Monte Carlo Scheme for the Bayesian Estimation of Parameters of α-stable Distributions},
author = {Eugenia Koblents and Joaqu\'{i}n M\'{i}guez and Marco A Rodr\'{i}guez and Alexandra M Schmidt},
url = {http://www.sciencedirect.com/science/article/pii/S0167947315002340},
doi = {10.1016/j.csda.2015.09.007},
issn = {01679473},
year = {2016},
date = {2016-03-01},
journal = {Computational Statistics \& Data Analysis},
volume = {95},
pages = {57--74},
abstract = {The class of $alpha$-stable distributions enjoys multiple practical applications in signal processing, finance, biology and other areas because it allows to describe interesting and complex data patterns, such as asymmetry or heavy tails, in contrast with the simpler and widely used Gaussian distribution. The density associated with a general $alpha$-stable distribution cannot be obtained in closed form, which hinders the process of estimating its parameters. A nonlinear population Monte Carlo (NPMC) scheme is applied in order to approximate the posterior probability distribution of the parameters of an $alpha$-stable random variable given a set of random realizations of the latter. The approximate posterior distribution is computed by way of an iterative algorithm and it consists of a collection of samples in the parameter space with associated nonlinearly-transformed importance weights. A numerical comparison of the main existing methods to estimate the $alpha$-stable parameters is provided, including the traditional frequentist techniques as well as a Markov chain Monte Carlo (MCMC) and a likelihood-free Bayesian approach. It is shown by means of computer simulations that the NPMC method outperforms the existing techniques in terms of parameter estimation error and failure rate for the whole range of values of $alpha$, including the smaller values for which most existing methods fail to work properly. Furthermore, it is shown that accurate parameter estimates can often be computed based on a low number of observations. Additionally, numerical results based on a set of real fish displacement data are provided.},
keywords = {Animal movement, Bayesian inference, Importance sampling, L{\'{e}}vy process, α-stable distributions},
pubstate = {published},
tppubtype = {article}
}
The class of $alpha$-stable distributions enjoys multiple practical applications in signal processing, finance, biology and other areas because it allows to describe interesting and complex data patterns, such as asymmetry or heavy tails, in contrast with the simpler and widely used Gaussian distribution. The density associated with a general $alpha$-stable distribution cannot be obtained in closed form, which hinders the process of estimating its parameters. A nonlinear population Monte Carlo (NPMC) scheme is applied in order to approximate the posterior probability distribution of the parameters of an $alpha$-stable random variable given a set of random realizations of the latter. The approximate posterior distribution is computed by way of an iterative algorithm and it consists of a collection of samples in the parameter space with associated nonlinearly-transformed importance weights. A numerical comparison of the main existing methods to estimate the $alpha$-stable parameters is provided, including the traditional frequentist techniques as well as a Markov chain Monte Carlo (MCMC) and a likelihood-free Bayesian approach. It is shown by means of computer simulations that the NPMC method outperforms the existing techniques in terms of parameter estimation error and failure rate for the whole range of values of $alpha$, including the smaller values for which most existing methods fail to work properly. Furthermore, it is shown that accurate parameter estimates can often be computed based on a low number of observations. Additionally, numerical results based on a set of real fish displacement data are provided.
2015
Martino, Luca; Elvira, Victor; Luengo, David; Corander, Jukka
An Adaptive Population Importance Sampler: Learning From Uncertainty Artículo de revista
En: IEEE Transactions on Signal Processing, vol. 63, no 16, pp. 4422–4437, 2015, ISSN: 1053-587X.
Resumen | Enlaces | BibTeX | Etiquetas: Adaptive importance sampling, adaptive multiple IS, adaptive population importance sampler, AMIS, APIS, Estimation, Importance sampling, IS estimators, iterative estimation, iterative methods, Journal, MC methods, Monte Carlo (MC) methods, Monte Carlo methods, population Monte Carlo, Proposals, Signal processing algorithms, simple temporal adaptation, Sociology, Standards, Wireless sensor network, Wireless Sensor Networks
@article{Martino2015bbb,
title = {An Adaptive Population Importance Sampler: Learning From Uncertainty},
author = {Luca Martino and Victor Elvira and David Luengo and Jukka Corander},
url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7117437},
doi = {10.1109/TSP.2015.2440215},
issn = {1053-587X},
year = {2015},
date = {2015-08-01},
journal = {IEEE Transactions on Signal Processing},
volume = {63},
number = {16},
pages = {4422--4437},
publisher = {IEEE},
abstract = {Monte Carlo (MC) methods are well-known computational techniques, widely used in different fields such as signal processing, communications and machine learning. An important class of MC methods is composed of importance sampling (IS) and its adaptive extensions, such as population Monte Carlo (PMC) and adaptive multiple IS (AMIS). In this paper, we introduce a novel adaptive and iterated importance sampler using a population of proposal densities. The proposed algorithm, named adaptive population importance sampling (APIS), provides a global estimation of the variables of interest iteratively, making use of all the samples previously generated. APIS combines a sophisticated scheme to build the IS estimators (based on the deterministic mixture approach) with a simple temporal adaptation (based on epochs). In this way, APIS is able to keep all the advantages of both AMIS and PMC, while minimizing their drawbacks. Furthermore, APIS is easily parallelizable. The cloud of proposals is adapted in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. The result is a fast, simple, robust, and high-performance algorithm applicable to a wide range of problems. Numerical results show the advantages of the proposed sampling scheme in four synthetic examples and a localization problem in a wireless sensor network.},
keywords = {Adaptive importance sampling, adaptive multiple IS, adaptive population importance sampler, AMIS, APIS, Estimation, Importance sampling, IS estimators, iterative estimation, iterative methods, Journal, MC methods, Monte Carlo (MC) methods, Monte Carlo methods, population Monte Carlo, Proposals, Signal processing algorithms, simple temporal adaptation, Sociology, Standards, Wireless sensor network, Wireless Sensor Networks},
pubstate = {published},
tppubtype = {article}
}
Monte Carlo (MC) methods are well-known computational techniques, widely used in different fields such as signal processing, communications and machine learning. An important class of MC methods is composed of importance sampling (IS) and its adaptive extensions, such as population Monte Carlo (PMC) and adaptive multiple IS (AMIS). In this paper, we introduce a novel adaptive and iterated importance sampler using a population of proposal densities. The proposed algorithm, named adaptive population importance sampling (APIS), provides a global estimation of the variables of interest iteratively, making use of all the samples previously generated. APIS combines a sophisticated scheme to build the IS estimators (based on the deterministic mixture approach) with a simple temporal adaptation (based on epochs). In this way, APIS is able to keep all the advantages of both AMIS and PMC, while minimizing their drawbacks. Furthermore, APIS is easily parallelizable. The cloud of proposals is adapted in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. The result is a fast, simple, robust, and high-performance algorithm applicable to a wide range of problems. Numerical results show the advantages of the proposed sampling scheme in four synthetic examples and a localization problem in a wireless sensor network.
Koblents, Eugenia; Miguez, Joaquin
A Population Monte Carlo Scheme with Transformed Weights and Its Application to Stochastic Kinetic Models Artículo de revista
En: Statistics and Computing, vol. 25, no 2, pp. 407–425, 2015, ISSN: 0960-3174.
Resumen | Enlaces | BibTeX | Etiquetas: COMPREHENSION, degeneracy of importance weights, Importance sampling, Journal, population Monte Carlo, Stochastic kinetic models
@article{Koblents2014b,
title = {A Population Monte Carlo Scheme with Transformed Weights and Its Application to Stochastic Kinetic Models},
author = {Eugenia Koblents and Joaquin Miguez},
url = {http://link.springer.com/10.1007/s11222-013-9440-2 http://gts.tsc.uc3m.es/wp-content/uploads/2014/01/NPMC_A-population-Monte-Carlo-scheme-with-transformed_jma.pdf},
doi = {10.1007/s11222-013-9440-2},
issn = {0960-3174},
year = {2015},
date = {2015-03-01},
journal = {Statistics and Computing},
volume = {25},
number = {2},
pages = {407--425},
abstract = {This paper addresses the Monte Carlo approximation of posterior probability distributions. In particular, we consider the population Monte Carlo (PMC) technique, which is based on an iterative importance sampling (IS) approach. An important drawback of this methodology is the degeneracy of the importance weights (IWs) when the dimension of either the observations or the variables of interest is high. To alleviate this difficulty, we propose a new method that performs a nonlinear transformation of the IWs. This operation reduces the weight variation, hence it avoids degeneracy and increases the efficiency of the IS scheme, specially when drawing from proposal functions which are poorly adapted to the true posterior. For the sake of illustration, we have applied the proposed algorithm to the estimation of the parameters of a Gaussian mixture model. This is a simple problem that enables us to discuss the main features of the proposed technique. As a practical application, we have also considered the challenging problem of estimating the rate parameters of a stochastic kinetic model (SKM). SKMs are multivariate systems that model molecular interactions in biological and chemical problems. We introduce a particularization of the proposed algorithm to SKMs and present numerical results.},
keywords = {COMPREHENSION, degeneracy of importance weights, Importance sampling, Journal, population Monte Carlo, Stochastic kinetic models},
pubstate = {published},
tppubtype = {article}
}
This paper addresses the Monte Carlo approximation of posterior probability distributions. In particular, we consider the population Monte Carlo (PMC) technique, which is based on an iterative importance sampling (IS) approach. An important drawback of this methodology is the degeneracy of the importance weights (IWs) when the dimension of either the observations or the variables of interest is high. To alleviate this difficulty, we propose a new method that performs a nonlinear transformation of the IWs. This operation reduces the weight variation, hence it avoids degeneracy and increases the efficiency of the IS scheme, specially when drawing from proposal functions which are poorly adapted to the true posterior. For the sake of illustration, we have applied the proposed algorithm to the estimation of the parameters of a Gaussian mixture model. This is a simple problem that enables us to discuss the main features of the proposed technique. As a practical application, we have also considered the challenging problem of estimating the rate parameters of a stochastic kinetic model (SKM). SKMs are multivariate systems that model molecular interactions in biological and chemical problems. We introduce a particularization of the proposed algorithm to SKMs and present numerical results.
2014
Koblents, Eugenia; Miguez, Joaquin
A Population Monte Carlo Scheme with Transformed Weights and Its Application to Stochastic Kinetic Models Artículo de revista
En: Statistics and Computing, no (to appear), 2014, ISSN: 0960-3174.
Resumen | Enlaces | BibTeX | Etiquetas: degeneracy of importance weights, Importance sampling, population Monte Carlo, Stochastic kinetic models
@article{Koblents2014bb,
title = {A Population Monte Carlo Scheme with Transformed Weights and Its Application to Stochastic Kinetic Models},
author = {Eugenia Koblents and Joaquin Miguez},
url = {http://link.springer.com/10.1007/s11222-013-9440-2 http://gts.tsc.uc3m.es/wp-content/uploads/2014/01/NPMC_A-population-Monte-Carlo-scheme-with-transformed_jma.pdf},
issn = {0960-3174},
year = {2014},
date = {2014-01-01},
journal = {Statistics and Computing},
number = {(to appear)},
abstract = {This paper addresses the Monte Carlo approximation of posterior probability distributions. In particular, we consider the population Monte Carlo (PMC) technique, which is based on an iterative importance sampling (IS) approach. An important drawback of this methodology is the degeneracy of the importance weights (IWs) when the dimension of either the observations or the variables of interest is high. To alleviate this difficulty, we propose a new method that performs a nonlinear transformation of the IWs. This operation reduces the weight variation, hence it avoids degeneracy and increases the efficiency of the IS scheme, specially when drawing from proposal functions which are poorly adapted to the true posterior. For the sake of illustration, we have applied the proposed algorithm to the estimation of the parameters of a Gaussian mixture model. This is a simple problem that enables us to discuss the main features of the proposed technique. As a practical application, we have also considered the challenging problem of estimating the rate parameters of a stochastic kinetic model (SKM). SKMs are multivariate systems that model molecular interactions in biological and chemical problems. We introduce a particularization of the proposed algorithm to SKMs and present numerical results.},
keywords = {degeneracy of importance weights, Importance sampling, population Monte Carlo, Stochastic kinetic models},
pubstate = {published},
tppubtype = {article}
}
This paper addresses the Monte Carlo approximation of posterior probability distributions. In particular, we consider the population Monte Carlo (PMC) technique, which is based on an iterative importance sampling (IS) approach. An important drawback of this methodology is the degeneracy of the importance weights (IWs) when the dimension of either the observations or the variables of interest is high. To alleviate this difficulty, we propose a new method that performs a nonlinear transformation of the IWs. This operation reduces the weight variation, hence it avoids degeneracy and increases the efficiency of the IS scheme, specially when drawing from proposal functions which are poorly adapted to the true posterior. For the sake of illustration, we have applied the proposed algorithm to the estimation of the parameters of a Gaussian mixture model. This is a simple problem that enables us to discuss the main features of the proposed technique. As a practical application, we have also considered the challenging problem of estimating the rate parameters of a stochastic kinetic model (SKM). SKMs are multivariate systems that model molecular interactions in biological and chemical problems. We introduce a particularization of the proposed algorithm to SKMs and present numerical results.