2015
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.
2013
Koblents, Eugenia; Miguez, Joaquin
A Population Monte Carlo Scheme for Computational Inference in High Dimensional Spaces Proceedings Article
En: 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 6318–6322, IEEE, Vancouver, 2013, ISSN: 1520-6149.
Resumen | Enlaces | BibTeX | Etiquetas: Approximation methods, computational inference, degeneracy of importance weights, high dimensional spaces, Importance sampling, importance weights, iterative importance sampling, iterative methods, mixture-PMC, mixture-PMC algorithm, Monte Carlo methods, MPMC, nonlinear transformations, population Monte Carlo, population Monte Carlo scheme, Probability density function, probability distributions, Proposals, Sociology, Standards
@inproceedings{Koblents2013a,
title = {A Population Monte Carlo Scheme for Computational Inference in High Dimensional Spaces},
author = {Eugenia Koblents and Joaquin Miguez},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6638881},
issn = {1520-6149},
year = {2013},
date = {2013-01-01},
booktitle = {2013 IEEE International Conference on Acoustics, Speech and Signal Processing},
pages = {6318--6322},
publisher = {IEEE},
address = {Vancouver},
abstract = {In this paper we address the Monte Carlo approximation of integrals with respect to probability distributions in high-dimensional spaces. In particular, we investigate the population Monte Carlo (PMC) scheme, which is based on an iterative importance sampling (IS) approach. Both IS and PMC suffer from the well known problem of degeneracy of the importance weights (IWs), which is closely related to the curse-of-dimensionality, and limits their applicability in large-scale practical problems. In this paper we investigate a novel PMC scheme that consists in performing nonlinear transformations of the IWs in order to smooth their variations and avoid degeneracy. We apply the modified IS scheme to the well-known mixture-PMC (MPMC) algorithm, which constructs the importance functions as mixtures of kernels. We present numerical results that show how the modified version of MPMC clearly outperforms the original scheme.},
keywords = {Approximation methods, computational inference, degeneracy of importance weights, high dimensional spaces, Importance sampling, importance weights, iterative importance sampling, iterative methods, mixture-PMC, mixture-PMC algorithm, Monte Carlo methods, MPMC, nonlinear transformations, population Monte Carlo, population Monte Carlo scheme, Probability density function, probability distributions, Proposals, Sociology, Standards},
pubstate = {published},
tppubtype = {inproceedings}
}
In this paper we address the Monte Carlo approximation of integrals with respect to probability distributions in high-dimensional spaces. In particular, we investigate the population Monte Carlo (PMC) scheme, which is based on an iterative importance sampling (IS) approach. Both IS and PMC suffer from the well known problem of degeneracy of the importance weights (IWs), which is closely related to the curse-of-dimensionality, and limits their applicability in large-scale practical problems. In this paper we investigate a novel PMC scheme that consists in performing nonlinear transformations of the IWs in order to smooth their variations and avoid degeneracy. We apply the modified IS scheme to the well-known mixture-PMC (MPMC) algorithm, which constructs the importance functions as mixtures of kernels. We present numerical results that show how the modified version of MPMC clearly outperforms the original scheme.