## 2016 |

## Journal Articles |

Valera, Isabel; Ruiz, Francisco J R; Perez-Cruz, Fernando Infinite Factorial Unbounded-State Hidden Markov Model Journal Article IEEE transactions on pattern analysis and machine intelligence, 38 (9), pp. 1816 – 1828, 2016, ISSN: 1939-3539. Abstract | Links | BibTeX | Tags: Bayes methods, Bayesian nonparametrics, CASI CAM CM, Computational modeling, GAMMA-L+ UC3M, Gibbs sampling, Hidden Markov models, Inference algorithms, Journal, Markov processes, Probability distribution, reversible jump Markov chain Monte Carlo, slice sampling, Time series, variational inference, Yttrium @article{Valera2016b, title = {Infinite Factorial Unbounded-State Hidden Markov Model}, author = {Isabel Valera and Francisco J R Ruiz and Fernando Perez-Cruz}, url = {http://www.ncbi.nlm.nih.gov/pubmed/26571511 http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=7322279}, doi = {10.1109/TPAMI.2015.2498931}, issn = {1939-3539}, year = {2016}, date = {2016-09-01}, journal = {IEEE transactions on pattern analysis and machine intelligence}, volume = {38}, number = {9}, pages = {1816 -- 1828}, abstract = {There are many scenarios in artificial intelligence, signal processing or medicine, in which a temporal sequence consists of several unknown overlapping independent causes, and we are interested in accurately recovering those canonical causes. Factorial hidden Markov models (FHMMs) present the versatility to provide a good fit to these scenarios. However, in some scenarios, the number of causes or the number of states of the FHMM cannot be known or limited a priori. In this paper, we propose an infinite factorial unbounded-state hidden Markov model (IFUHMM), in which the number of parallel hidden Markov models (HMMs) and states in each HMM are potentially unbounded. We rely on a Bayesian nonparametric (BNP) prior over integer-valued matrices, in which the columns represent the Markov chains, the rows the time indexes, and the integers the state for each chain and time instant. First, we extend the existent infinite factorial binary-state HMM to allow for any number of states. Then, we modify this model to allow for an unbounded number of states and derive an MCMC-based inference algorithm that properly deals with the trade-off between the unbounded number of states and chains. We illustrate the performance of our proposed models in the power disaggregation problem.}, keywords = {Bayes methods, Bayesian nonparametrics, CASI CAM CM, Computational modeling, GAMMA-L+ UC3M, Gibbs sampling, Hidden Markov models, Inference algorithms, Journal, Markov processes, Probability distribution, reversible jump Markov chain Monte Carlo, slice sampling, Time series, variational inference, Yttrium}, pubstate = {published}, tppubtype = {article} } There are many scenarios in artificial intelligence, signal processing or medicine, in which a temporal sequence consists of several unknown overlapping independent causes, and we are interested in accurately recovering those canonical causes. Factorial hidden Markov models (FHMMs) present the versatility to provide a good fit to these scenarios. However, in some scenarios, the number of causes or the number of states of the FHMM cannot be known or limited a priori. In this paper, we propose an infinite factorial unbounded-state hidden Markov model (IFUHMM), in which the number of parallel hidden Markov models (HMMs) and states in each HMM are potentially unbounded. We rely on a Bayesian nonparametric (BNP) prior over integer-valued matrices, in which the columns represent the Markov chains, the rows the time indexes, and the integers the state for each chain and time instant. First, we extend the existent infinite factorial binary-state HMM to allow for any number of states. Then, we modify this model to allow for an unbounded number of states and derive an MCMC-based inference algorithm that properly deals with the trade-off between the unbounded number of states and chains. We illustrate the performance of our proposed models in the power disaggregation problem. |

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 = {Alfredo Nazábal and Pablo Garcia-Moreno and Antonio Artés-Rodríguez and Zoubin Ghahramani}, 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. |

Vazquez-Vilar, Gonzalo; Campo, Adria Tauste; i Fabregas, Albert Guillen; Martinez, Alfonso Bayesian M-Ary Hypothesis Testing: The Meta-Converse and Verdú-Han Bounds Are Tight Journal Article IEEE Transactions on Information Theory, 62 (5), pp. 2324–2333, 2016, ISSN: 0018-9448. Abstract | Links | BibTeX | Tags: Bayes methods, Channel Coding, Electronic mail, error probability, Journal, Random variables, Testing @article{Vazquez-Vilar2016, title = {Bayesian M-Ary Hypothesis Testing: The Meta-Converse and Verdú-Han Bounds Are Tight}, author = {Gonzalo Vazquez-Vilar and Adria Tauste Campo and Albert Guillen i Fabregas and Alfonso Martinez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7434042}, doi = {10.1109/TIT.2016.2542080}, issn = {0018-9448}, year = {2016}, date = {2016-05-01}, journal = {IEEE Transactions on Information Theory}, volume = {62}, number = {5}, pages = {2324--2333}, abstract = {Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy et al.; the second expression is a function of an information-spectrum measure and implies the tightness of a generalized Verdú-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose.}, keywords = {Bayes methods, Channel Coding, Electronic mail, error probability, Journal, Random variables, Testing}, pubstate = {published}, tppubtype = {article} } Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy et al.; the second expression is a function of an information-spectrum measure and implies the tightness of a generalized Verdú-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose. |

Valera, Isabel; Ruiz, Francisco J R; Perez-Cruz, Fernando Infinite Factorial Unbounded-State Hidden Markov Model Journal Article IEEE transactions on pattern analysis and machine intelligence, To appear (99), pp. 1, 2016, ISSN: 1939-3539. Abstract | Links | BibTeX | Tags: Bayes methods, Bayesian nonparametrics, CASI CAM CM, Computational modeling, GAMMA-L+ UC3M, Gibbs sampling, Hidden Markov models, Inference algorithms, Markov processes, Probability distribution, reversible jump Markov chain Monte Carlo, slice sampling, Time series, variational inference, Yttrium @article{Valera2016c, title = {Infinite Factorial Unbounded-State Hidden Markov Model}, author = {Isabel Valera and Francisco J R Ruiz and Fernando Perez-Cruz}, url = {http://www.ncbi.nlm.nih.gov/pubmed/26571511 http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=7322279}, doi = {10.1109/TPAMI.2015.2498931}, issn = {1939-3539}, year = {2016}, date = {2016-01-01}, journal = {IEEE transactions on pattern analysis and machine intelligence}, volume = {To appear}, number = {99}, pages = {1}, abstract = {There are many scenarios in artificial intelligence, signal processing or medicine, in which a temporal sequence consists of several unknown overlapping independent causes, and we are interested in accurately recovering those canonical causes. Factorial hidden Markov models (FHMMs) present the versatility to provide a good fit to these scenarios. However, in some scenarios, the number of causes or the number of states of the FHMM cannot be known or limited a priori. In this paper, we propose an infinite factorial unbounded-state hidden Markov model (IFUHMM), in which the number of parallel hidden Markov models (HMMs) and states in each HMM are potentially unbounded. We rely on a Bayesian nonparametric (BNP) prior over integer-valued matrices, in which the columns represent the Markov chains, the rows the time indexes, and the integers the state for each chain and time instant. First, we extend the existent infinite factorial binary-state HMM to allow for any number of states. Then, we modify this model to allow for an unbounded number of states and derive an MCMC-based inference algorithm that properly deals with the trade-off between the unbounded number of states and chains. We illustrate the performance of our proposed models in the power disaggregation problem.}, keywords = {Bayes methods, Bayesian nonparametrics, CASI CAM CM, Computational modeling, GAMMA-L+ UC3M, Gibbs sampling, Hidden Markov models, Inference algorithms, Markov processes, Probability distribution, reversible jump Markov chain Monte Carlo, slice sampling, Time series, variational inference, Yttrium}, pubstate = {published}, tppubtype = {article} } There are many scenarios in artificial intelligence, signal processing or medicine, in which a temporal sequence consists of several unknown overlapping independent causes, and we are interested in accurately recovering those canonical causes. Factorial hidden Markov models (FHMMs) present the versatility to provide a good fit to these scenarios. However, in some scenarios, the number of causes or the number of states of the FHMM cannot be known or limited a priori. In this paper, we propose an infinite factorial unbounded-state hidden Markov model (IFUHMM), in which the number of parallel hidden Markov models (HMMs) and states in each HMM are potentially unbounded. We rely on a Bayesian nonparametric (BNP) prior over integer-valued matrices, in which the columns represent the Markov chains, the rows the time indexes, and the integers the state for each chain and time instant. First, we extend the existent infinite factorial binary-state HMM to allow for any number of states. Then, we modify this model to allow for an unbounded number of states and derive an MCMC-based inference algorithm that properly deals with the trade-off between the unbounded number of states and chains. We illustrate the performance of our proposed models in the power disaggregation problem. |

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{Nazabal2016b, title = {Human Activity Recognition by Combining a Small Number of Classifiers}, author = {Alfredo Nazabal and Pablo Garcia-Moreno and Antonio Artes-Rodriguez and Zoubin Ghahramani}, 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 |

Luengo, David; Martino, Luca; Elvira, Victor; Bugallo, Monica F Bias correction for distributed Bayesian estimators Inproceedings 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pp. 253–256, IEEE, Cancun, 2015, ISBN: 978-1-4799-1963-5. Abstract | Links | BibTeX | Tags: Bayes methods, Big data, Distributed databases, Estimation, Probability density function, Wireless Sensor Networks @inproceedings{Luengo2015a, title = {Bias correction for distributed Bayesian estimators}, author = {David Luengo and Luca Martino and Victor Elvira and Monica F Bugallo}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7383784}, doi = {10.1109/CAMSAP.2015.7383784}, isbn = {978-1-4799-1963-5}, year = {2015}, date = {2015-12-01}, booktitle = {2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)}, pages = {253--256}, publisher = {IEEE}, address = {Cancun}, abstract = {Dealing with the whole dataset in big data estimation problems is usually unfeasible. A common solution then consists of dividing the data into several smaller sets, performing distributed Bayesian estimation and combining these partial estimates to obtain a global estimate. A major problem of this approach is the presence of a non-negligible bias in the partial estimators, due to the mismatch between the unknown true prior and the prior assumed in the estimation. A simple method to mitigate the effect of this bias is proposed in this paper. Essentially, the approach is based on using a reference data set to obtain a rough estimation of the parameter of interest, i.e., a reference parameter. This information is then communicated to the partial filters that handle the smaller data sets, which can thus use a refined prior centered around this parameter. Simulation results confirm the good performance of this scheme.}, keywords = {Bayes methods, Big data, Distributed databases, Estimation, Probability density function, Wireless Sensor Networks}, pubstate = {published}, tppubtype = {inproceedings} } Dealing with the whole dataset in big data estimation problems is usually unfeasible. A common solution then consists of dividing the data into several smaller sets, performing distributed Bayesian estimation and combining these partial estimates to obtain a global estimate. A major problem of this approach is the presence of a non-negligible bias in the partial estimators, due to the mismatch between the unknown true prior and the prior assumed in the estimation. A simple method to mitigate the effect of this bias is proposed in this paper. Essentially, the approach is based on using a reference data set to obtain a rough estimation of the parameter of interest, i.e., a reference parameter. This information is then communicated to the partial filters that handle the smaller data sets, which can thus use a refined prior centered around this parameter. Simulation results confirm the good performance of this scheme. |

Valera, Isabel; Ruiz, Francisco J R; Svensson, Lennart; Perez-Cruz, Fernando A Bayesian Nonparametric Approach for Blind Multiuser Channel Estimation Inproceedings 2015 23rd European Signal Processing Conference (EUSIPCO), pp. 2766–2770, IEEE, Nice, 2015, ISBN: 978-0-9928-6263-3. Abstract | Links | BibTeX | Tags: Bayes methods, Bayesian nonparametric, communication systems, factorial HMM, Hidden Markov models, machine-to-machine, multiuser communication, Receiving antennas, Signal to noise ratio, Transmitters @inproceedings{Valera2015b, title = {A Bayesian Nonparametric Approach for Blind Multiuser Channel Estimation}, author = {Isabel Valera and Francisco J R Ruiz and Lennart Svensson and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7362888 http://www.eurasip.org/Proceedings/Eusipco/Eusipco2015/papers/1570096659.pdf}, doi = {10.1109/EUSIPCO.2015.7362888}, isbn = {978-0-9928-6263-3}, year = {2015}, date = {2015-08-01}, booktitle = {2015 23rd European Signal Processing Conference (EUSIPCO)}, pages = {2766--2770}, publisher = {IEEE}, address = {Nice}, abstract = {In many modern multiuser communication systems, users are allowed to enter and leave the system at any given time. Thus, the number of active users is an unknown and time-varying parameter, and the performance of the system depends on how accurately this parameter is estimated over time. We address the problem of blind joint channel parameter and data estimation in a multiuser communication channel in which the number of transmitters is not known. For that purpose, we develop a Bayesian nonparametric model based on the Markov Indian buffet process and an inference algorithm that makes use of slice sampling and particle Gibbs with ancestor sampling. Our experimental results show that the proposed approach can effectively recover the data-generating process for a wide range of scenarios.}, keywords = {Bayes methods, Bayesian nonparametric, communication systems, factorial HMM, Hidden Markov models, machine-to-machine, multiuser communication, Receiving antennas, Signal to noise ratio, Transmitters}, pubstate = {published}, tppubtype = {inproceedings} } In many modern multiuser communication systems, users are allowed to enter and leave the system at any given time. Thus, the number of active users is an unknown and time-varying parameter, and the performance of the system depends on how accurately this parameter is estimated over time. We address the problem of blind joint channel parameter and data estimation in a multiuser communication channel in which the number of transmitters is not known. For that purpose, we develop a Bayesian nonparametric model based on the Markov Indian buffet process and an inference algorithm that makes use of slice sampling and particle Gibbs with ancestor sampling. Our experimental results show that the proposed approach can effectively recover the data-generating process for a wide range of scenarios. |

## 2014 |

## Journal Articles |

Read, Jesse; Bielza, Concha; Larranaga, Pedro Multi-Dimensional Classification with Super-Classes Journal Article IEEE Transactions on Knowledge and Data Engineering, 26 (7), pp. 1720–1733, 2014, ISSN: 1041-4347. Abstract | Links | BibTeX | Tags: Accuracy, Bayes methods, Classification, COMPRHENSION, conditional dependence, Context, core goals, data instance, evaluation metrics, Integrated circuit modeling, modeling class dependencies, multi-dimensional, Multi-dimensional classification, multidimensional classification problem, multidimensional datasets, multidimensional learners, multilabel classification, multilabel research, multiple class variables, ordinary class, pattern classification, problem transformation, recently-popularized task, super classes, super-class partitions, tractable running time, Training, Vectors @article{Read2014b, title = {Multi-Dimensional Classification with Super-Classes}, author = {Jesse Read and Concha Bielza and Pedro Larranaga}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6648319}, issn = {1041-4347}, year = {2014}, date = {2014-01-01}, journal = {IEEE Transactions on Knowledge and Data Engineering}, volume = {26}, number = {7}, pages = {1720--1733}, publisher = {IEEE}, abstract = {The multi-dimensional classification problem is a generalisation of the recently-popularised task of multi-label classification, where each data instance is associated with multiple class variables. There has been relatively little research carried out specific to multi-dimensional classification and, although one of the core goals is similar (modelling dependencies among classes), there are important differences; namely a higher number of possible classifications. In this paper we present method for multi-dimensional classification, drawing from the most relevant multi-label research, and combining it with important novel developments. Using a fast method to model the conditional dependence between class variables, we form super-class partitions and use them to build multi-dimensional learners, learning each super-class as an ordinary class, and thus explicitly modelling class dependencies. Additionally, we present a mechanism to deal with the many class values inherent to super-classes, and thus make learning efficient. To investigate the effectiveness of this approach we carry out an empirical evaluation on a range of multi-dimensional datasets, under different evaluation metrics, and in comparison with high-performing existing multi-dimensional approaches from the literature. Analysis of results shows that our approach offers important performance gains over competing methods, while also exhibiting tractable running time.}, keywords = {Accuracy, Bayes methods, Classification, COMPRHENSION, conditional dependence, Context, core goals, data instance, evaluation metrics, Integrated circuit modeling, modeling class dependencies, multi-dimensional, Multi-dimensional classification, multidimensional classification problem, multidimensional datasets, multidimensional learners, multilabel classification, multilabel research, multiple class variables, ordinary class, pattern classification, problem transformation, recently-popularized task, super classes, super-class partitions, tractable running time, Training, Vectors}, pubstate = {published}, tppubtype = {article} } The multi-dimensional classification problem is a generalisation of the recently-popularised task of multi-label classification, where each data instance is associated with multiple class variables. There has been relatively little research carried out specific to multi-dimensional classification and, although one of the core goals is similar (modelling dependencies among classes), there are important differences; namely a higher number of possible classifications. In this paper we present method for multi-dimensional classification, drawing from the most relevant multi-label research, and combining it with important novel developments. Using a fast method to model the conditional dependence between class variables, we form super-class partitions and use them to build multi-dimensional learners, learning each super-class as an ordinary class, and thus explicitly modelling class dependencies. Additionally, we present a mechanism to deal with the many class values inherent to super-classes, and thus make learning efficient. To investigate the effectiveness of this approach we carry out an empirical evaluation on a range of multi-dimensional datasets, under different evaluation metrics, and in comparison with high-performing existing multi-dimensional approaches from the literature. Analysis of results shows that our approach offers important performance gains over competing methods, while also exhibiting tractable running time. |

## Inproceedings |

Valera, Isabel; Ruiz, Francisco J R; Perez-Cruz, Fernando Infinite Factorial Unbounded Hidden Markov Model for Blind Multiuser Channel Estimation Inproceedings 2014 4th International Workshop on Cognitive Information Processing (CIP), pp. 1–6, IEEE, Copenhagen, 2014, ISBN: 978-1-4799-3696-0. Abstract | Links | BibTeX | Tags: Bayes methods, Bayesian non parametrics, Bayesian nonparametric models, blind multiuser channel estimation, Channel estimation, degrees of freedom, detection problems, dispersive channel model, generative model, Hidden Markov models, HMM, inference algorithm, infinite factorial unbounded hidden Markov model, Markov chain Monte Carlo, Markov processes, MIMO, MIMO communication, MIMO communication systems, multiple-input multiple-output (MIMO), multiple-input multiple-output communication syste, receiver performance, Receivers, Signal to noise ratio, Transmitters, unbounded channel length, unbounded number, user detection @inproceedings{Valera2014a, title = {Infinite Factorial Unbounded Hidden Markov Model for Blind Multiuser Channel Estimation}, author = {Isabel Valera and Francisco J R Ruiz and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6844506}, isbn = {978-1-4799-3696-0}, year = {2014}, date = {2014-01-01}, booktitle = {2014 4th International Workshop on Cognitive Information Processing (CIP)}, pages = {1--6}, publisher = {IEEE}, address = {Copenhagen}, abstract = {Bayesian nonparametric models allow solving estimation and detection problems with an unbounded number of degrees of freedom. In multiuser multiple-input multiple-output (MIMO) communication systems we might not know the number of active users and the channel they face, and assuming maximal scenarios (maximum number of transmitters and maximum channel length) might degrade the receiver performance. In this paper, we propose a Bayesian nonparametric prior and its associated inference algorithm, which is able to detect an unbounded number of users with an unbounded channel length. This generative model provides the dispersive channel model for each user and a probabilistic estimate for each transmitted symbol in a fully blind manner, i.e., without the need of pilot (training) symbols.}, keywords = {Bayes methods, Bayesian non parametrics, Bayesian nonparametric models, blind multiuser channel estimation, Channel estimation, degrees of freedom, detection problems, dispersive channel model, generative model, Hidden Markov models, HMM, inference algorithm, infinite factorial unbounded hidden Markov model, Markov chain Monte Carlo, Markov processes, MIMO, MIMO communication, MIMO communication systems, multiple-input multiple-output (MIMO), multiple-input multiple-output communication syste, receiver performance, Receivers, Signal to noise ratio, Transmitters, unbounded channel length, unbounded number, user detection}, pubstate = {published}, tppubtype = {inproceedings} } Bayesian nonparametric models allow solving estimation and detection problems with an unbounded number of degrees of freedom. In multiuser multiple-input multiple-output (MIMO) communication systems we might not know the number of active users and the channel they face, and assuming maximal scenarios (maximum number of transmitters and maximum channel length) might degrade the receiver performance. In this paper, we propose a Bayesian nonparametric prior and its associated inference algorithm, which is able to detect an unbounded number of users with an unbounded channel length. This generative model provides the dispersive channel model for each user and a probabilistic estimate for each transmitted symbol in a fully blind manner, i.e., without the need of pilot (training) symbols. |

## 2013 |

## Journal Articles |

Vazquez, Manuel A; Miguez, Joaquin User Activity Tracking in DS-CDMA Systems Journal Article IEEE Transactions on Vehicular Technology, 62 (7), pp. 3188–3203, 2013, ISSN: 0018-9545. Abstract | Links | BibTeX | Tags: Activity detection, activity tracking, Bayes methods, Bayesian framework, Channel estimation, code division multiple access, code-division multiple access (CDMA), computer simulations, data detection, direct sequence code division multiple-access, DS-CDMA systems, Equations, joint channel and data estimation, joint channel estimation, Joints, MAP equalizers, Mathematical model, maximum a posteriori, MIMO communication, Multiaccess communication, multiple-input-multiple-output communication chann, multiuser communication systems, per-survivor processing (PSP), radio receivers, Receivers, sequential Monte Carlo (SMC) methods, time-varying number, time-varying parameter, Vectors, wireless channels @article{Vazquez2013a, title = {User Activity Tracking in DS-CDMA Systems}, author = {Manuel A Vazquez and Joaquin Miguez}, url = {http://www.tsc.uc3m.es/~jmiguez/papers/P39_2013_User Activity Tracking in DS-CDMA Systems.pdf http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6473922}, issn = {0018-9545}, year = {2013}, date = {2013-01-01}, journal = {IEEE Transactions on Vehicular Technology}, volume = {62}, number = {7}, pages = {3188--3203}, abstract = {In modern multiuser communication systems, users are allowed to enter or leave the system at any given time. Thus, the number of active users is an unknown and time-varying parameter, and the performance of the system depends on how accurately this parameter is estimated over time. The so-called problem of user identification, which consists of determining the number and identities of users transmitting in a communication system, is usually solved prior to, and hence independently of, that posed by the detection of the transmitted data. Since both problems are tightly connected, a joint solution is desirable. In this paper, we focus on direct-sequence (DS) code-division multiple-access (CDMA) systems and derive, within a Bayesian framework, different receivers that cope with an unknown and time-varying number of users while performing joint channel estimation and data detection. The main feature of these receivers, compared with other recently proposed schemes for user activity detection, is that they are natural extensions of existing maximum a posteriori (MAP) equalizers for multiple-input-multiple-output communication channels. We assess the validity of the proposed receivers, including their reliability in detecting the number and identities of active users, by way of computer simulations.}, keywords = {Activity detection, activity tracking, Bayes methods, Bayesian framework, Channel estimation, code division multiple access, code-division multiple access (CDMA), computer simulations, data detection, direct sequence code division multiple-access, DS-CDMA systems, Equations, joint channel and data estimation, joint channel estimation, Joints, MAP equalizers, Mathematical model, maximum a posteriori, MIMO communication, Multiaccess communication, multiple-input-multiple-output communication chann, multiuser communication systems, per-survivor processing (PSP), radio receivers, Receivers, sequential Monte Carlo (SMC) methods, time-varying number, time-varying parameter, Vectors, wireless channels}, pubstate = {published}, tppubtype = {article} } In modern multiuser communication systems, users are allowed to enter or leave the system at any given time. Thus, the number of active users is an unknown and time-varying parameter, and the performance of the system depends on how accurately this parameter is estimated over time. The so-called problem of user identification, which consists of determining the number and identities of users transmitting in a communication system, is usually solved prior to, and hence independently of, that posed by the detection of the transmitted data. Since both problems are tightly connected, a joint solution is desirable. In this paper, we focus on direct-sequence (DS) code-division multiple-access (CDMA) systems and derive, within a Bayesian framework, different receivers that cope with an unknown and time-varying number of users while performing joint channel estimation and data detection. The main feature of these receivers, compared with other recently proposed schemes for user activity detection, is that they are natural extensions of existing maximum a posteriori (MAP) equalizers for multiple-input-multiple-output communication channels. We assess the validity of the proposed receivers, including their reliability in detecting the number and identities of active users, by way of computer simulations. |

## 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 = {Luis Salamanca and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz}, 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. |

## Inproceedings |

O'Mahony, Niamh; Perez-Cruz, Fernando A novel Sequential Bayesian Approach to GPS Acquisition 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: Bayes methods, coarse synchronization, Correlators, data acquisition, Delay, Doppler effect, Global Positioning System, GPS acquisition, GPS signal parameters, learning (artificial intelligence), online learning algorithm, Receivers, Satellites, sequential Bayesian approach, signal acquisition, signal detection, Synchronization @inproceedings{O'Mahony2012, title = {A novel Sequential Bayesian Approach to GPS Acquisition}, author = {Niamh O'Mahony and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6232921}, 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 work, a novel online learning algorithm is presented for the synchronization of Global Positioning System (GPS) signal parameters at the acquisition, or coarse synchronization, stage. The algorithm is based on a Bayesian approach, which has, to date, not been exploited for the acquisition problem. Simulated results are presented to illustrate the algorithm performance, in terms of accuracy and acquisition time, along with results from the acquisition of signals from live GPS satellites using both the new algorithm and a state-of-the-art approach for comparison.}, keywords = {Bayes methods, coarse synchronization, Correlators, data acquisition, Delay, Doppler effect, Global Positioning System, GPS acquisition, GPS signal parameters, learning (artificial intelligence), online learning algorithm, Receivers, Satellites, sequential Bayesian approach, signal acquisition, signal detection, Synchronization}, pubstate = {published}, tppubtype = {inproceedings} } In this work, a novel online learning algorithm is presented for the synchronization of Global Positioning System (GPS) signal parameters at the acquisition, or coarse synchronization, stage. The algorithm is based on a Bayesian approach, which has, to date, not been exploited for the acquisition problem. Simulated results are presented to illustrate the algorithm performance, in terms of accuracy and acquisition time, along with results from the acquisition of signals from live GPS satellites using both the new algorithm and a state-of-the-art approach for comparison. |

## 2010 |

## Inproceedings |

Vinuelas-Peris, Pablo; Artés-Rodríguez, Antonio Bayesian Joint Recovery of Correlated Signals in Distributed Compressed Sensing Inproceedings 2010 2nd International Workshop on Cognitive Information Processing, pp. 382–387, IEEE, Elba, 2010, ISBN: 978-1-4244-6459-3. Abstract | Links | BibTeX | Tags: Bayes methods, Bayesian joint recovery, Bayesian methods, correlated signal, Correlation, correlation methods, Covariance matrix, Dictionaries, distributed compressed sensing, matrix decomposition, Noise measurement, sensors, sparse component correlation coefficient @inproceedings{Vinuelas-Peris2010, title = {Bayesian Joint Recovery of Correlated Signals in Distributed Compressed Sensing}, author = {Pablo Vinuelas-Peris and Antonio Artés-Rodríguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5604103}, isbn = {978-1-4244-6459-3}, year = {2010}, date = {2010-01-01}, booktitle = {2010 2nd International Workshop on Cognitive Information Processing}, pages = {382--387}, publisher = {IEEE}, address = {Elba}, abstract = {In this paper we address the problem of Distributed Compressed Sensing (DCS) of correlated signals. We model the correlation using the sparse components correlation coefficient of signals, a general and simple measure. We develop an sparse Bayesian learning method for this setting, that can be applied to both random and optimized projection matrices. As a result, we obtain a reduction of the number of measurements needed for a given recovery error that is dependent on the correlation coefficient, as shown by computer simulations in different scenarios.}, keywords = {Bayes methods, Bayesian joint recovery, Bayesian methods, correlated signal, Correlation, correlation methods, Covariance matrix, Dictionaries, distributed compressed sensing, matrix decomposition, Noise measurement, sensors, sparse component correlation coefficient}, pubstate = {published}, tppubtype = {inproceedings} } In this paper we address the problem of Distributed Compressed Sensing (DCS) of correlated signals. We model the correlation using the sparse components correlation coefficient of signals, a general and simple measure. We develop an sparse Bayesian learning method for this setting, that can be applied to both random and optimized projection matrices. As a result, we obtain a reduction of the number of measurements needed for a given recovery error that is dependent on the correlation coefficient, as shown by computer simulations in different scenarios. |

Salamanca, Luis; Murillo-Fuentes, Juan Jose; Perez-Cruz, Fernando Bayesian BCJR for Channel Equalization and Decoding Inproceedings 2010 IEEE International Workshop on Machine Learning for Signal Processing, pp. 53–58, IEEE, Kittila, 2010, ISSN: 1551-2541. Abstract | Links | BibTeX | Tags: a posteriori probability, Bayes methods, Bayesian BCJR, Bayesian methods, Bit error rate, channel decoding, channel estate information, Channel estimation, Decoding, digital communication, digital communications, equalisers, Equalizers, error statistics, Markov processes, Maximum likelihood decoding, maximum likelihood estimation, multipath channel, probabilistic channel equalization, Probability, single input single output model, SISO model, statistical information, Training @inproceedings{Salamanca2010, title = {Bayesian BCJR for Channel Equalization and Decoding}, author = {Luis Salamanca and Juan Jose Murillo-Fuentes and Fernando Perez-Cruz}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5589201}, issn = {1551-2541}, year = {2010}, date = {2010-01-01}, booktitle = {2010 IEEE International Workshop on Machine Learning for Signal Processing}, pages = {53--58}, publisher = {IEEE}, address = {Kittila}, abstract = {In this paper we focus on the probabilistic channel equalization in digital communications. We face the single input single output (SISO) model to show how the statistical information about the multipath channel can be exploited to further improve our estimation of the a posteriori probabilities (APP) during the equalization process. We consider not only the uncertainty due to the noise in the channel, but also in the estimate of the channel estate information (CSI). Thus, we resort to a Bayesian approach for the computation of the APP. This novel algorithm has the same complexity as the BCJR, exhibiting lower bit error rate at the output of the channel decoder than the standard BCJR that considers maximum likelihood (ML) to estimate the CSI.}, keywords = {a posteriori probability, Bayes methods, Bayesian BCJR, Bayesian methods, Bit error rate, channel decoding, channel estate information, Channel estimation, Decoding, digital communication, digital communications, equalisers, Equalizers, error statistics, Markov processes, Maximum likelihood decoding, maximum likelihood estimation, multipath channel, probabilistic channel equalization, Probability, single input single output model, SISO model, statistical information, Training}, pubstate = {published}, tppubtype = {inproceedings} } In this paper we focus on the probabilistic channel equalization in digital communications. We face the single input single output (SISO) model to show how the statistical information about the multipath channel can be exploited to further improve our estimation of the a posteriori probabilities (APP) during the equalization process. We consider not only the uncertainty due to the noise in the channel, but also in the estimate of the channel estate information (CSI). Thus, we resort to a Bayesian approach for the computation of the APP. This novel algorithm has the same complexity as the BCJR, exhibiting lower bit error rate at the output of the channel decoder than the standard BCJR that considers maximum likelihood (ML) to estimate the CSI. |

## 2009 |

## Inproceedings |

Martino, Luca; Miguez, Joaquin A Novel Rejection Sampling Scheme for Posterior Probability Distributions Inproceedings 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 2921–2924, IEEE, Taipei, 2009, ISSN: 1520-6149. Abstract | Links | BibTeX | Tags: Additive noise, arbitrary target probability distributions, Bayes methods, Bayesian methods, Monte Carlo integration, Monte Carlo methods, Monte Carlo techniques, Overbounding, posterior probability distributions, Probability density function, Probability distribution, Proposals, Rejection sampling, rejection sampling scheme, Sampling methods, Signal processing algorithms, signal sampling, Upper bound @inproceedings{Martino2009, title = {A Novel Rejection Sampling Scheme for Posterior Probability Distributions}, author = {Luca Martino and Joaquin Miguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4960235}, issn = {1520-6149}, year = {2009}, date = {2009-01-01}, booktitle = {2009 IEEE International Conference on Acoustics, Speech and Signal Processing}, pages = {2921--2924}, publisher = {IEEE}, address = {Taipei}, abstract = {Rejection sampling (RS) is a well-known method to draw from arbitrary target probability distributions, which has important applications by itself or as a building block for more sophisticated Monte Carlo techniques. The main limitation to the use of RS is the need to find an adequate upper bound for the ratio of the target probability density function (pdf) over the proposal pdf from which the samples are generated. There are no general methods to analytically find this bound, except in the particular case in which the target pdf is log-concave. In this paper we adopt a Bayesian view of the problem and propose a general RS scheme to draw from the posterior pdf of a signal of interest using its prior density as a proposal function. The method enables the analytical calculation of the bound and can be applied to a large class of target densities. We illustrate its use with a simple numerical example.}, keywords = {Additive noise, arbitrary target probability distributions, Bayes methods, Bayesian methods, Monte Carlo integration, Monte Carlo methods, Monte Carlo techniques, Overbounding, posterior probability distributions, Probability density function, Probability distribution, Proposals, Rejection sampling, rejection sampling scheme, Sampling methods, Signal processing algorithms, signal sampling, Upper bound}, pubstate = {published}, tppubtype = {inproceedings} } Rejection sampling (RS) is a well-known method to draw from arbitrary target probability distributions, which has important applications by itself or as a building block for more sophisticated Monte Carlo techniques. The main limitation to the use of RS is the need to find an adequate upper bound for the ratio of the target probability density function (pdf) over the proposal pdf from which the samples are generated. There are no general methods to analytically find this bound, except in the particular case in which the target pdf is log-concave. In this paper we adopt a Bayesian view of the problem and propose a general RS scheme to draw from the posterior pdf of a signal of interest using its prior density as a proposal function. The method enables the analytical calculation of the bound and can be applied to a large class of target densities. We illustrate its use with a simple numerical example. |