## 2017 |

## Journal Articles |

Elvira, Victor ; Martino, Luca ; Luengo, David ; Bugallo, Monica F Improving Population Monte Carlo: Alternative Weighting and Resampling Schemes Journal Article Signal Processing, 131 , pp. 77–91, 2017, ISSN: 01651684. Abstract | Links | BibTeX | Tags: Adaptive importance sampling, Journal, population Monte Carlo, Proposal distribution, Resampling @article{Elvira2017, title = {Improving Population Monte Carlo: Alternative Weighting and Resampling Schemes}, author = {Elvira, Victor and Martino, Luca and Luengo, David and Bugallo, Monica F.}, url = {http://www.sciencedirect.com/science/article/pii/S0165168416301633}, doi = {10.1016/j.sigpro.2016.07.012}, issn = {01651684}, year = {2017}, date = {2017-02-01}, journal = {Signal Processing}, volume = {131}, pages = {77--91}, abstract = {Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal distribution and assign them weights according to the importance sampling principle. Critical issues in applying PMC methods are the choice of the generating functions for the samples and the avoidance of the sample degeneracy. In this paper, we propose three new schemes that considerably improve the performance of the original PMC formulation by allowing for better exploration of the space of unknowns and by selecting more adequately the surviving samples. A theoretical analysis is performed, proving the superiority of the novel schemes in terms of variance of the associated estimators and preservation of the sample diversity. Furthermore, we show that they outperform other state of the art algorithms (both in terms of mean square error and robustness w.r.t. initialization) through extensive numerical simulations.}, keywords = {Adaptive importance sampling, Journal, population Monte Carlo, Proposal distribution, Resampling}, pubstate = {published}, tppubtype = {article} } Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal distribution and assign them weights according to the importance sampling principle. Critical issues in applying PMC methods are the choice of the generating functions for the samples and the avoidance of the sample degeneracy. In this paper, we propose three new schemes that considerably improve the performance of the original PMC formulation by allowing for better exploration of the space of unknowns and by selecting more adequately the surviving samples. A theoretical analysis is performed, proving the superiority of the novel schemes in terms of variance of the associated estimators and preservation of the sample diversity. Furthermore, we show that they outperform other state of the art algorithms (both in terms of mean square error and robustness w.r.t. initialization) through extensive numerical simulations. |

## 2015 |

## Journal Articles |

Martino, Luca ; Elvira, Victor ; Luengo, David ; Corander, J An Adaptive Population Importance Sampler: Learning From Uncertainty Journal Article IEEE Transactions on Signal Processing, 63 (16), pp. 4422–4437, 2015, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: 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{Martino2015b, title = {An Adaptive Population Importance Sampler: Learning From Uncertainty}, author = {Martino, Luca and Elvira, Victor and Luengo, David and Corander, J.}, 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 Journal Article Statistics and Computing, 25 (2), pp. 407–425, 2015, ISSN: 0960-3174. Abstract | Links | BibTeX | Tags: 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 = {Koblents, Eugenia and Miguez, Joaquin}, 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 |

## Journal Articles |

Koblents, Eugenia ; Miguez, Joaquin A Population Monte Carlo Scheme with Transformed Weights and Its Application to Stochastic Kinetic Models Journal Article Statistics and Computing, ((to appear)), 2014, ISSN: 0960-3174. Abstract | Links | BibTeX | Tags: degeneracy of importance weights, Importance sampling, population Monte Carlo, Stochastic kinetic models @article{Koblents2014, title = {A Population Monte Carlo Scheme with Transformed Weights and Its Application to Stochastic Kinetic Models}, author = {Koblents, Eugenia and Miguez, Joaquin}, 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. |

## Inproceedings |

Martino, Luca ; Elvira, Víctor ; Luengo, David ; Artés-Rodríguez, Antonio ; Carander, Jukka Orthogonal MCMC Algorithms Inproceedings 2014 IEEE Workshop on Statistical Signal Processing (SSP 2014), Gold Coast, 2014. Abstract | Links | BibTeX | Tags: Bayesian inference, Markov Chain Monte Carlo (MCMC), Parallel Chains, population Monte Carlo @inproceedings{Martino2014b, title = {Orthogonal MCMC Algorithms}, author = {Martino, Luca and Elvira, Víctor and Luengo, David and Artés-Rodríguez, Antonio and Carander, Jukka}, url = {http://edas.info/p15153#S1569490857}, year = {2014}, date = {2014-01-01}, booktitle = {2014 IEEE Workshop on Statistical Signal Processing (SSP 2014)}, address = {Gold Coast}, abstract = {Monte Carlo (MC) methods are widely used in signal processing, machine learning and stochastic optimization. A wellknown class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce a novel parallel interacting MCMC scheme, where the parallel chains share information using another MCMC technique working on the entire population of current states. These parallel “vertical” chains are led by random-walk proposals, whereas the “horizontal” MCMC uses a independent proposal, which can be easily adapted by making use of all the generated samples. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error, as well as robustness w.r.t. to initial values and parameter choice.}, keywords = {Bayesian inference, Markov Chain Monte Carlo (MCMC), Parallel Chains, population Monte Carlo}, pubstate = {published}, tppubtype = {inproceedings} } Monte Carlo (MC) methods are widely used in signal processing, machine learning and stochastic optimization. A wellknown class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce a novel parallel interacting MCMC scheme, where the parallel chains share information using another MCMC technique working on the entire population of current states. These parallel “vertical” chains are led by random-walk proposals, whereas the “horizontal” MCMC uses a independent proposal, which can be easily adapted by making use of all the generated samples. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error, as well as robustness w.r.t. to initial values and parameter choice. |

## 2013 |

## Inproceedings |

Koblents, Eugenia ; Miguez, Joaquin A Population Monte Carlo Scheme for Computational Inference in High Dimensional Spaces Inproceedings 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 6318–6322, IEEE, Vancouver, 2013, ISSN: 1520-6149. Abstract | Links | BibTeX | Tags: 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 = {Koblents, Eugenia and Miguez, Joaquin}, 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. |