## 2015 |

## Journal Articles |

Elvira, Victor; Martino, Luca; Luengo, David; Bugallo, Monica F Efficient Multiple Importance Sampling Estimators Journal Article IEEE Signal Processing Letters, 22 (10), pp. 1757–1761, 2015, ISSN: 1070-9908. Abstract | Links | BibTeX | Tags: Adaptive importance sampling, classical mixture approach, computational complexity, Computational efficiency, Computer Simulation, deterministic mixture, estimation theory, Journal, Monte Carlo methods, multiple importance sampling, multiple importance sampling estimator, partial deterministic mixture MIS estimator, Proposals, signal sampling, Sociology, Standards, variance reduction, weight calculation @article{Elvira2015bb, title = {Efficient Multiple Importance Sampling Estimators}, author = {Victor Elvira and Luca Martino and David Luengo and Monica F Bugallo}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7105865}, doi = {10.1109/LSP.2015.2432078}, issn = {1070-9908}, year = {2015}, date = {2015-10-01}, journal = {IEEE Signal Processing Letters}, volume = {22}, number = {10}, pages = {1757--1761}, publisher = {IEEE}, abstract = {Multiple importance sampling (MIS) methods use a set of proposal distributions from which samples are drawn. Each sample is then assigned an importance weight that can be obtained according to different strategies. This work is motivated by the trade-off between variance reduction and computational complexity of the different approaches (classical vs. deterministic mixture) available for the weight calculation. A new method that achieves an efficient compromise between both factors is introduced in this letter. It is based on forming a partition of the set of proposal distributions and computing the weights accordingly. Computer simulations show the excellent performance of the associated partial deterministic mixture MIS estimator.}, keywords = {Adaptive importance sampling, classical mixture approach, computational complexity, Computational efficiency, Computer Simulation, deterministic mixture, estimation theory, Journal, Monte Carlo methods, multiple importance sampling, multiple importance sampling estimator, partial deterministic mixture MIS estimator, Proposals, signal sampling, Sociology, Standards, variance reduction, weight calculation}, pubstate = {published}, tppubtype = {article} } Multiple importance sampling (MIS) methods use a set of proposal distributions from which samples are drawn. Each sample is then assigned an importance weight that can be obtained according to different strategies. This work is motivated by the trade-off between variance reduction and computational complexity of the different approaches (classical vs. deterministic mixture) available for the weight calculation. A new method that achieves an efficient compromise between both factors is introduced in this letter. It is based on forming a partition of the set of proposal distributions and computing the weights accordingly. Computer simulations show the excellent performance of the associated partial deterministic mixture MIS estimator. |

Martino, Luca; Elvira, Victor; Luengo, David; Corander, Jukka 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{Martino2015bb, 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. |

## Inproceedings |

Fernandez-Bes, Jesus; Elvira, Victor; Vaerenbergh, Steven Van A Probabilistic Least-Mean-Squares Filter Inproceedings 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 2199–2203, IEEE, Brisbane, 2015, ISBN: 978-1-4673-6997-8. Abstract | Links | BibTeX | Tags: adaptable step size LMS algorithm, Adaptation models, adaptive filtering, Approximation algorithms, Bayesian machine learning techniques, efficient approximation algorithm, filtering theory, Least squares approximations, least-mean-squares, probabilistic least mean squares filter, Probabilistic logic, probabilisticmodels, Probability, Signal processing algorithms, Standards, state-space models @inproceedings{Fernandez-Bes2015, title = {A Probabilistic Least-Mean-Squares Filter}, author = {Jesus Fernandez-Bes and Victor Elvira and Steven Van Vaerenbergh}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7178361 http://www.tsc.uc3m.es/~velvira/papers/ICASSP2015_bes.pdf}, doi = {10.1109/ICASSP.2015.7178361}, isbn = {978-1-4673-6997-8}, year = {2015}, date = {2015-04-01}, booktitle = {2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, pages = {2199--2203}, publisher = {IEEE}, address = {Brisbane}, abstract = {We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the proposed approximation preserves the linear complexity of the standard LMS. Numerical results show the improved performance of the algorithm with respect to standard LMS and state-of-the-art algorithms with similar complexity. The goal of this work, therefore, is to open the door to bring somemore Bayesian machine learning techniques to adaptive filtering.}, keywords = {adaptable step size LMS algorithm, Adaptation models, adaptive filtering, Approximation algorithms, Bayesian machine learning techniques, efficient approximation algorithm, filtering theory, Least squares approximations, least-mean-squares, probabilistic least mean squares filter, Probabilistic logic, probabilisticmodels, Probability, Signal processing algorithms, Standards, state-space models}, pubstate = {published}, tppubtype = {inproceedings} } We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the proposed approximation preserves the linear complexity of the standard LMS. Numerical results show the improved performance of the algorithm with respect to standard LMS and state-of-the-art algorithms with similar complexity. The goal of this work, therefore, is to open the door to bring somemore Bayesian machine learning techniques to adaptive filtering. |

## 2013 |

## Journal Articles |

Leiva-Murillo, Jose M; Gomez-Chova, Luis; Camps-Valls, Gustavo Multitask Remote Sensing Data Classification Journal Article IEEE Transactions on Geoscience and Remote Sensing, 51 (1), pp. 151–161, 2013, ISSN: 0196-2892. Links | BibTeX | Tags: Aggregates, angular image features, Cloud screening, covariate shift, covariate shift (CS), cross information, data processing problems, data set bias, domain adaptation, geophysical image processing, Hilbert space pairwise predictor Euclidean distanc, image classification, image feature nonstationary behavior, Kernel, land mine detection, land-mine detection, learning (artificial intelligence), Machine learning, matrix decomposition, matrix regularization, MTL, multisource image classification, multispectral images, multitask learning, multitask learning (MTL), multitask remote sensing data classification, multitemporal classification, multitemporal image classification, radar data, regularization schemes, relational operators, Remote sensing, small sample set problem, spatial image features, Standards, support vector machine, support vector machine (SVM), Support vector machines, SVM, temporal image features, Training, urban monitoring @article{Leiva-Murillo2013a, title = {Multitask Remote Sensing Data Classification}, author = {Jose M Leiva-Murillo and Luis Gomez-Chova and Gustavo Camps-Valls}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6214595}, issn = {0196-2892}, year = {2013}, date = {2013-01-01}, journal = {IEEE Transactions on Geoscience and Remote Sensing}, volume = {51}, number = {1}, pages = {151--161}, publisher = {IEEE}, keywords = {Aggregates, angular image features, Cloud screening, covariate shift, covariate shift (CS), cross information, data processing problems, data set bias, domain adaptation, geophysical image processing, Hilbert space pairwise predictor Euclidean distanc, image classification, image feature nonstationary behavior, Kernel, land mine detection, land-mine detection, learning (artificial intelligence), Machine learning, matrix decomposition, matrix regularization, MTL, multisource image classification, multispectral images, multitask learning, multitask learning (MTL), multitask remote sensing data classification, multitemporal classification, multitemporal image classification, radar data, regularization schemes, relational operators, Remote sensing, small sample set problem, spatial image features, Standards, support vector machine, support vector machine (SVM), Support vector machines, SVM, temporal image features, Training, urban monitoring}, pubstate = {published}, tppubtype = {article} } |

## 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 = {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. |

## 2012 |

## Inproceedings |

Garcia-Moreno, Pablo; Artés-Rodríguez, Antonio; Hansen, Lars Kai A Hold-out Method to Correct PCA Variance Inflation Inproceedings 2012 3rd International Workshop on Cognitive Information Processing (CIP), pp. 1–6, IEEE, Baiona, 2012, ISBN: 978-1-4673-1878-5. Abstract | Links | BibTeX | Tags: Approximation methods, classification scenario, computational complexity, computational cost, Computational efficiency, correction method, hold-out method, hold-out procedure, leave-one-out procedure, LOO method, LOO procedure, Mathematical model, PCA algorithm, PCA variance inflation, Principal component analysis, singular value decomposition, Standards, SVD, Training @inproceedings{Garcia-Moreno2012, title = {A Hold-out Method to Correct PCA Variance Inflation}, author = {Pablo Garcia-Moreno and Antonio Artés-Rodríguez and Lars Kai Hansen}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6232926}, isbn = {978-1-4673-1878-5}, year = {2012}, date = {2012-01-01}, booktitle = {2012 3rd International Workshop on Cognitive Information Processing (CIP)}, pages = {1--6}, publisher = {IEEE}, address = {Baiona}, abstract = {In this paper we analyze the problem of variance inflation experienced by the PCA algorithm when working in an ill-posed scenario where the dimensionality of the training set is larger than its sample size. In an earlier article a correction method based on a Leave-One-Out (LOO) procedure was introduced. We propose a Hold-out procedure whose computational cost is lower and, unlike the LOO method, the number of SVD's does not scale with the sample size. We analyze its properties from a theoretical and empirical point of view. Finally we apply it to a real classification scenario.}, keywords = {Approximation methods, classification scenario, computational complexity, computational cost, Computational efficiency, correction method, hold-out method, hold-out procedure, leave-one-out procedure, LOO method, LOO procedure, Mathematical model, PCA algorithm, PCA variance inflation, Principal component analysis, singular value decomposition, Standards, SVD, Training}, pubstate = {published}, tppubtype = {inproceedings} } In this paper we analyze the problem of variance inflation experienced by the PCA algorithm when working in an ill-posed scenario where the dimensionality of the training set is larger than its sample size. In an earlier article a correction method based on a Leave-One-Out (LOO) procedure was introduced. We propose a Hold-out procedure whose computational cost is lower and, unlike the LOO method, the number of SVD's does not scale with the sample size. We analyze its properties from a theoretical and empirical point of view. Finally we apply it to a real classification scenario. |