## 2016 |

## Journal Articles |

Martino, Luca; Elvira, Victor; Luengo, David; Corander, Jukka; Louzada, Francisco Orthogonal Parallel MCMC Methods for Sampling and Optimization (Journal Article) Digital Signal Processing, 58 , pp. 64–84, 2016, ISSN: 10512004. (Abstract | Links | BibTeX | Tags: Bayesian inference, Block Independent Metropolis, Journal, Optimization, Parallel Markov Chain Monte Carlo, Parallel Multiple Try Metropolis, Parallel Simulated Annealing, Recycling samples) @article{Martino2016b, title = {Orthogonal Parallel MCMC Methods for Sampling and Optimization}, author = {Martino, Luca and Elvira, Victor and Luengo, David and Corander, Jukka and Louzada, Francisco}, url = {http://www.sciencedirect.com/science/article/pii/S1051200416300987}, doi = {10.1016/j.dsp.2016.07.013}, issn = {10512004}, year = {2016}, date = {2016-11-01}, journal = {Digital Signal Processing}, volume = {58}, pages = {64--84}, abstract = {Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called orthogonal MCMC (O-MCMC), where a set of “vertical” parallel MCMC chains share information using some “horizontal” MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes in order to reduce the overall computational cost of parallel multiple try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel simulated annealing (SA) algorithms. Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and the choice of the parameters.}, keywords = {Bayesian inference, Block Independent Metropolis, Journal, Optimization, Parallel Markov Chain Monte Carlo, Parallel Multiple Try Metropolis, Parallel Simulated Annealing, Recycling samples}, pubstate = {published}, tppubtype = {article} } Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called orthogonal MCMC (O-MCMC), where a set of “vertical” parallel MCMC chains share information using some “horizontal” MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes in order to reduce the overall computational cost of parallel multiple try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel simulated annealing (SA) algorithms. Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and the choice of the parameters. |

Nazábal, Alfredo; Garcia-Moreno, Pablo; Artés-Rodríguez, Antonio; Ghahramani, Zoubin Human Activity Recognition by Combining a Small Number of Classifiers. (Journal Article) IEEE journal of biomedical and health informatics, 20 (5), pp. 1342 – 1351, 2016, ISSN: 2168-2208. (Abstract | Links | BibTeX | Tags: Bayes methods, Bayesian inference, Biological system modeling, Classifier combination, Databases, Estimation, Hidden Markov models, Journal, Sensor systems) @article{Nazabal2016b, title = {Human Activity Recognition by Combining a Small Number of Classifiers.}, author = {Nazábal, Alfredo and Garcia-Moreno, Pablo and Artés-Rodríguez, Antonio and Ghahramani, Zoubin}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7161292}, doi = {10.1109/JBHI.2015.2458274}, issn = {2168-2208}, year = {2016}, date = {2016-09-01}, journal = {IEEE journal of biomedical and health informatics}, volume = {20}, number = {5}, pages = {1342 -- 1351}, publisher = {IEEE}, abstract = {We consider the problem of daily Human Activity Recognition (HAR) using multiple wireless inertial sensors and, specifically, HAR systems with a very low number of sensors, each one providing an estimation of the performed activities. We propose new Bayesian models to combine the output of the sensors. The models are based on a soft outputs combination of individual classifiers to deal with the small number of sensors. We also incorporate the dynamic nature of human activities as a first order homogeneous Markov chain. We develop both inductive and transductive inference methods for each model to be employed in supervised and semi-supervised situations, respectively. Using different real HAR databases, we compare our classifiers combination models against a single classifier that employs all the signals from the sensors. Our models exhibit consistently a reduction of the error rate and an increase of robustness against sensor failures. Our models also outperform other classifiers combination models that do not consider soft outputs and a Markovian structure of the human activities.}, keywords = {Bayes methods, Bayesian inference, Biological system modeling, Classifier combination, Databases, Estimation, Hidden Markov models, Journal, Sensor systems}, pubstate = {published}, tppubtype = {article} } We consider the problem of daily Human Activity Recognition (HAR) using multiple wireless inertial sensors and, specifically, HAR systems with a very low number of sensors, each one providing an estimation of the performed activities. We propose new Bayesian models to combine the output of the sensors. The models are based on a soft outputs combination of individual classifiers to deal with the small number of sensors. We also incorporate the dynamic nature of human activities as a first order homogeneous Markov chain. We develop both inductive and transductive inference methods for each model to be employed in supervised and semi-supervised situations, respectively. Using different real HAR databases, we compare our classifiers combination models against a single classifier that employs all the signals from the sensors. Our models exhibit consistently a reduction of the error rate and an increase of robustness against sensor failures. Our models also outperform other classifiers combination models that do not consider soft outputs and a Markovian structure of the human activities. |

Koblents, Eugenia; Míguez, Joaquín; Rodríguez, Marco; Schmidt, Alexandra A Nonlinear Population Monte Carlo Scheme for the Bayesian Estimation of Parameters of α-stable Distributions (Journal Article) Computational Statistics & Data Analysis, 95 , pp. 57–74, 2016, ISSN: 01679473. (Abstract | Links | BibTeX | Tags: 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 = {Koblents, Eugenia and Míguez, Joaquín and Rodríguez, Marco A. and Schmidt, Alexandra M.}, 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{é}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. |

Nazabal, Alfredo; Garcia-Moreno, Pablo; Artes-Rodriguez, Antonio; Ghahramani, Zoubin Human Activity Recognition by Combining a Small Number of Classifiers (Journal Article) IEEE journal of biomedical and health informatics, To appear , 2016, ISSN: 2168-2208. (Abstract | Links | BibTeX | Tags: Bayes methods, Bayesian inference, Biological system modeling, Classifier combination, Databases, Estimation, Hidden Markov models, Sensor systems) @article{Nazabal2016, title = {Human Activity Recognition by Combining a Small Number of Classifiers}, author = {Nazabal, Alfredo and Garcia-Moreno, Pablo and Artes-Rodriguez, Antonio and Ghahramani, Zoubin}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7161292}, doi = {10.1109/JBHI.2015.2458274}, issn = {2168-2208}, year = {2016}, date = {2016-01-01}, journal = {IEEE journal of biomedical and health informatics}, volume = {To appear}, publisher = {IEEE}, abstract = {We consider the problem of daily Human Activity Recognition (HAR) using multiple wireless inertial sensors and, specifically, HAR systems with a very low number of sensors, each one providing an estimation of the performed activities. We propose new Bayesian models to combine the output of the sensors. The models are based on a soft outputs combination of individual classifiers to deal with the small number of sensors. We also incorporate the dynamic nature of human activities as a first order homogeneous Markov chain. We develop both inductive and transductive inference methods for each model to be employed in supervised and semi-supervised situations, respectively. Using different real HAR databases, we compare our classifiers combination models against a single classifier that employs all the signals from the sensors. Our models exhibit consistently a reduction of the error rate and an increase of robustness against sensor failures. Our models also outperform other classifiers combination models that do not consider soft outputs and a Markovian structure of the human activities.}, keywords = {Bayes methods, Bayesian inference, Biological system modeling, Classifier combination, Databases, Estimation, Hidden Markov models, Sensor systems}, pubstate = {published}, tppubtype = {article} } We consider the problem of daily Human Activity Recognition (HAR) using multiple wireless inertial sensors and, specifically, HAR systems with a very low number of sensors, each one providing an estimation of the performed activities. We propose new Bayesian models to combine the output of the sensors. The models are based on a soft outputs combination of individual classifiers to deal with the small number of sensors. We also incorporate the dynamic nature of human activities as a first order homogeneous Markov chain. We develop both inductive and transductive inference methods for each model to be employed in supervised and semi-supervised situations, respectively. Using different real HAR databases, we compare our classifiers combination models against a single classifier that employs all the signals from the sensors. Our models exhibit consistently a reduction of the error rate and an increase of robustness against sensor failures. Our models also outperform other classifiers combination models that do not consider soft outputs and a Markovian structure of the human activities. |

## 2015 |

## Inproceedings |

Martino, Luca; Elvira, Victor; Luengo, David; Corander, Jukka Parallel interacting Markov adaptive importance sampling (Inproceeding) 2015 23rd European Signal Processing Conference (EUSIPCO), pp. 499–503, IEEE, Nice, 2015, ISBN: 978-0-9928-6263-3. (Abstract | Links | BibTeX | Tags: Adaptive importance sampling, Bayesian inference, MCMC methods, Monte Carlo methods, Parallel Chains, Probability density function, Proposals, Signal processing, Signal processing algorithms, Sociology) @inproceedings{Martino2015b, title = {Parallel interacting Markov adaptive importance sampling}, author = {Martino, Luca and Elvira, Victor and Luengo, David and Corander, Jukka}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7362433 http://www.eurasip.org/Proceedings/Eusipco/Eusipco2015/papers/1570111267.pdf}, doi = {10.1109/EUSIPCO.2015.7362433}, isbn = {978-0-9928-6263-3}, year = {2015}, date = {2015-08-01}, booktitle = {2015 23rd European Signal Processing Conference (EUSIPCO)}, pages = {499--503}, publisher = {IEEE}, address = {Nice}, abstract = {Monte Carlo (MC) methods are widely used for statistical inference in signal processing applications. A well-known class of MC methods is importance sampling (IS) and its adaptive extensions. In this work, we introduce an iterated importance sampler using a population of proposal densities, which are adapted according to an MCMC technique over the population of location parameters. The novel algorithm provides a global estimation of the variables of interest iteratively, using all the samples weighted according to the deterministic mixture scheme. Numerical results, on a multi-modal example and a localization problem in wireless sensor networks, show the advantages of the proposed schemes.}, keywords = {Adaptive importance sampling, Bayesian inference, MCMC methods, Monte Carlo methods, Parallel Chains, Probability density function, Proposals, Signal processing, Signal processing algorithms, Sociology}, pubstate = {published}, tppubtype = {inproceedings} } Monte Carlo (MC) methods are widely used for statistical inference in signal processing applications. A well-known class of MC methods is importance sampling (IS) and its adaptive extensions. In this work, we introduce an iterated importance sampler using a population of proposal densities, which are adapted according to an MCMC technique over the population of location parameters. The novel algorithm provides a global estimation of the variables of interest iteratively, using all the samples weighted according to the deterministic mixture scheme. Numerical results, on a multi-modal example and a localization problem in wireless sensor networks, show the advantages of the proposed schemes. |

Martino, Luca; Elvira, Victor; Luengo, David; Artés-Rodríguez, Antonio; Corander, Smelly Parallel MCMC Chains (Inproceeding) 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4070–4074, IEEE, Brisbane, 2015, ISBN: 978-1-4673-6997-8. (Abstract | Links | BibTeX | Tags: Bayesian inference, learning (artificial intelligence), Machine learning, Markov chain Monte Carlo, Markov chain Monte Carlo algorithms, Markov processes, MC methods, MCMC algorithms, MCMC scheme, mean square error, mean square error methods, Monte Carlo methods, optimisation, parallel and interacting chains, Probability density function, Proposals, robustness, Sampling methods, Signal processing, Signal processing algorithms, signal sampling, smelly parallel chains, smelly parallel MCMC chains, Stochastic optimization) @inproceedings{Martino2015a, title = {Smelly Parallel MCMC Chains}, author = {Martino, Luca and Elvira, Victor and Luengo, David and Artés-Rodríguez, Antonio and Corander, J.}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7178736 http://www.tsc.uc3m.es/~velvira/papers/ICASSP2015_martino.pdf}, doi = {10.1109/ICASSP.2015.7178736}, 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 = {4070--4074}, publisher = {IEEE}, address = {Brisbane}, abstract = {Monte Carlo (MC) methods are useful tools for Bayesian inference and stochastic optimization that have been widely applied in signal processing and machine learning. A well-known 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, thus yielding a faster exploration of the state space. The interaction is carried out generating a dynamic repulsion among the “smelly” parallel chains that takes into account the entire population of current states. The ergodicity of the scheme and its relationship with other sampling methods are discussed. Numerical results show the advantages of the proposed approach in terms of mean square error, robustness w.r.t. to initial values and parameter choice.}, keywords = {Bayesian inference, learning (artificial intelligence), Machine learning, Markov chain Monte Carlo, Markov chain Monte Carlo algorithms, Markov processes, MC methods, MCMC algorithms, MCMC scheme, mean square error, mean square error methods, Monte Carlo methods, optimisation, parallel and interacting chains, Probability density function, Proposals, robustness, Sampling methods, Signal processing, Signal processing algorithms, signal sampling, smelly parallel chains, smelly parallel MCMC chains, Stochastic optimization}, pubstate = {published}, tppubtype = {inproceedings} } Monte Carlo (MC) methods are useful tools for Bayesian inference and stochastic optimization that have been widely applied in signal processing and machine learning. A well-known 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, thus yielding a faster exploration of the state space. The interaction is carried out generating a dynamic repulsion among the “smelly” parallel chains that takes into account the entire population of current states. The ergodicity of the scheme and its relationship with other sampling methods are discussed. Numerical results show the advantages of the proposed approach in terms of mean square error, robustness w.r.t. to initial values and parameter choice. |

## 2014 |

## Journal Articles |

Impedovo, Sebastiano; Liu, Cheng-Lin; Impedovo, Donato; Pirlo, Giuseppe; Read, Jesse; Martino, Luca; Luengo, David Efficient Monte Carlo Methods for Multi-Dimensional Learning with Classifier Chains (Journal Article) Pattern Recognition, 47 (3), pp. 1535–1546, 2014. (Abstract | Links | BibTeX | Tags: Bayesian inference, Classifier chains, Monte Carlo methods, Multi-dimensional classification, Multi-label classification) @article{Impedovo2014b, title = {Efficient Monte Carlo Methods for Multi-Dimensional Learning with Classifier Chains}, author = {Impedovo, Sebastiano and Liu, Cheng-Lin and Impedovo, Donato and Pirlo, Giuseppe and Read, Jesse and Martino, Luca and Luengo, David}, url = {http://www.sciencedirect.com/science/article/pii/S0031320313004160}, year = {2014}, date = {2014-01-01}, journal = {Pattern Recognition}, volume = {47}, number = {3}, pages = {1535--1546}, abstract = {Multi-dimensional classification (MDC) is the supervised learning problem where an instance is associated with multiple classes, rather than with a single class, as in traditional classification problems. Since these classes are often strongly correlated, modeling the dependencies between them allows MDC methods to improve their performance – at the expense of an increased computational cost. In this paper we focus on the classifier chains (CC) approach for modeling dependencies, one of the most popular and highest-performing methods for multi-label classification (MLC), a particular case of MDC which involves only binary classes (i.e., labels). The original CC algorithm makes a greedy approximation, and is fast but tends to propagate errors along the chain. Here we present novel Monte Carlo schemes, both for finding a good chain sequence and performing efficient inference. Our algorithms remain tractable for high-dimensional data sets and obtain the best predictive performance across several real data sets.}, keywords = {Bayesian inference, Classifier chains, Monte Carlo methods, Multi-dimensional classification, Multi-label classification}, pubstate = {published}, tppubtype = {article} } Multi-dimensional classification (MDC) is the supervised learning problem where an instance is associated with multiple classes, rather than with a single class, as in traditional classification problems. Since these classes are often strongly correlated, modeling the dependencies between them allows MDC methods to improve their performance – at the expense of an increased computational cost. In this paper we focus on the classifier chains (CC) approach for modeling dependencies, one of the most popular and highest-performing methods for multi-label classification (MLC), a particular case of MDC which involves only binary classes (i.e., labels). The original CC algorithm makes a greedy approximation, and is fast but tends to propagate errors along the chain. Here we present novel Monte Carlo schemes, both for finding a good chain sequence and performing efficient inference. Our algorithms remain tractable for high-dimensional data sets and obtain the best predictive performance across several real data sets. |

## Inproceedings |

Martino, Luca; Elvira, Víctor; Luengo, David; Artés-Rodríguez, Antonio; Carander, Jukka Orthogonal MCMC Algorithms (Inproceeding) 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 |

Read, Jesse; Martino, Luca; Luengo, David Eficient Monte Carlo Optimization for Multi-Label Classifier Chains (Inproceeding) ICASSP 2013: The 38th International Conference on Acoustics, Speech, and Signal Processing, Vancouver, 2013. (Abstract | BibTeX | Tags: Bayesian inference, Classifier chains, Monte Carlo methods, Multi-dimensional classification, Multi-label classification) @inproceedings{Read2013, title = {Eficient Monte Carlo Optimization for Multi-Label Classifier Chains}, author = {Read, Jesse and Martino, Luca and Luengo, David}, year = {2013}, date = {2013-01-01}, booktitle = {ICASSP 2013: The 38th International Conference on Acoustics, Speech, and Signal Processing}, address = {Vancouver}, abstract = {Multi-dimensional classification (MDC) is the supervised learning problem where an instance is associated with multiple classes, rather than with a single class, as in traditional classification problems. Since these classes are often strongly correlated, modeling the dependencies between them allows MDC methods to improve their performance at the expense of an increased computational cost. In this paper we focus on the classifier chains (CC) approach for modeling dependencies, one of the most popular and highest- performing methods for multi-label classification (MLC), a particular case of MDC which involves only binary classes (i.e., labels). The original CC algorithm makes a greedy approximation, and is fast but tends to propagate errors along the chain. Here we present novel Monte Carlo schemes, both for nding a good chain sequence and performing ecient inference. Our algorithms remain tractable for high-dimensional data sets and obtain the best predictive performance across several real data sets.}, keywords = {Bayesian inference, Classifier chains, Monte Carlo methods, Multi-dimensional classification, Multi-label classification}, pubstate = {published}, tppubtype = {inproceedings} } Multi-dimensional classification (MDC) is the supervised learning problem where an instance is associated with multiple classes, rather than with a single class, as in traditional classification problems. Since these classes are often strongly correlated, modeling the dependencies between them allows MDC methods to improve their performance at the expense of an increased computational cost. In this paper we focus on the classifier chains (CC) approach for modeling dependencies, one of the most popular and highest- performing methods for multi-label classification (MLC), a particular case of MDC which involves only binary classes (i.e., labels). The original CC algorithm makes a greedy approximation, and is fast but tends to propagate errors along the chain. Here we present novel Monte Carlo schemes, both for nding a good chain sequence and performing ecient inference. Our algorithms remain tractable for high-dimensional data sets and obtain the best predictive performance across several real data sets. |

## 2012 |

## Journal Articles |

Salamanca, Luis; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando Bayesian Equalization for LDPC Channel Decoding (Journal Article) IEEE Transactions on Signal Processing, 60 (5), pp. 2672–2676, 2012, ISSN: 1053-587X. (Abstract | Links | BibTeX | Tags: Approximation methods, Bayes methods, Bayesian equalization, Bayesian estimation problem, Bayesian inference, Bayesian methods, BCJR (Bahl–Cocke–Jelinek–Raviv) algorithm, BCJR algorithm, Channel Coding, channel decoding, channel equalization, channel equalization problem, Channel estimation, channel state information, CSI, Decoding, equalisers, Equalizers, expectation propagation, expectation propagation algorithm, fading channels, graphical model representation, intersymbol interference, Kullback-Leibler divergence, LDPC, LDPC coding, low-density parity-check decoder, Modulation, parity check codes, symbol posterior estimates, Training) @article{Salamanca2012b, title = {Bayesian Equalization for LDPC Channel Decoding}, author = {Salamanca, Luis and Murillo-Fuentes, Juan Jose and Perez-Cruz, Fernando}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6129544}, issn = {1053-587X}, year = {2012}, date = {2012-01-01}, journal = {IEEE Transactions on Signal Processing}, volume = {60}, number = {5}, pages = {2672--2676}, abstract = {We describe the channel equalization problem, and its prior estimate of the channel state information (CSI), as a joint Bayesian estimation problem to improve each symbol posterior estimates at the input of the channel decoder. Our approach takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate. However, this solution cannot be computed in linear time, because it depends on all the transmitted symbols. Hence, we also put forward an approximation for each symbol's posterior, using the expectation propagation algorithm, which is optimal from the Kullback-Leibler divergence viewpoint and yields an equalization with a complexity identical to the BCJR algorithm. We also use a graphical model representation of the full posterior, in which the proposed approximation can be readily understood. The proposed posterior estimates are more accurate than those computed using the ML estimate for the CSI. In order to illustrate this point, we measure the error rate at the output of a low-density parity-check decoder, which needs the exact posterior for each symbol to detect the incoming word and it is sensitive to a mismatch in those posterior estimates. For example, for QPSK modulation and a channel with three taps, we can expect gains over 0.5 dB with same computational complexity as the ML receiver.}, keywords = {Approximation methods, Bayes methods, Bayesian equalization, Bayesian estimation problem, Bayesian inference, Bayesian methods, BCJR (Bahl–Cocke–Jelinek–Raviv) algorithm, BCJR algorithm, Channel Coding, channel decoding, channel equalization, channel equalization problem, Channel estimation, channel state information, CSI, Decoding, equalisers, Equalizers, expectation propagation, expectation propagation algorithm, fading channels, graphical model representation, intersymbol interference, Kullback-Leibler divergence, LDPC, LDPC coding, low-density parity-check decoder, Modulation, parity check codes, symbol posterior estimates, Training}, pubstate = {published}, tppubtype = {article} } We describe the channel equalization problem, and its prior estimate of the channel state information (CSI), as a joint Bayesian estimation problem to improve each symbol posterior estimates at the input of the channel decoder. Our approach takes into consideration not only the uncertainty due to the noise in the channel, but also the uncertainty in the CSI estimate. However, this solution cannot be computed in linear time, because it depends on all the transmitted symbols. Hence, we also put forward an approximation for each symbol's posterior, using the expectation propagation algorithm, which is optimal from the Kullback-Leibler divergence viewpoint and yields an equalization with a complexity identical to the BCJR algorithm. We also use a graphical model representation of the full posterior, in which the proposed approximation can be readily understood. The proposed posterior estimates are more accurate than those computed using the ML estimate for the CSI. In order to illustrate this point, we measure the error rate at the output of a low-density parity-check decoder, which needs the exact posterior for each symbol to detect the incoming word and it is sensitive to a mismatch in those posterior estimates. For example, for QPSK modulation and a channel with three taps, we can expect gains over 0.5 dB with same computational complexity as the ML receiver. |