## 2016 |

## Journal Articles |

Valera, Isabel; Ruiz, Francisco; 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 = {Valera, Isabel and Ruiz, Francisco J. R. and Perez-Cruz, Fernando}, 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. |

Valera, Isabel; Ruiz, Francisco; 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{Valera2016, title = {Infinite Factorial Unbounded-State Hidden Markov Model}, author = {Valera, Isabel and Ruiz, Francisco J. R. and Perez-Cruz, Fernando}, 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. |

## 2012 |

## Journal Articles |

Maiz, Cristina; Molanes-Lopez, Elisa; Miguez, Joaquin; Djuric, Petar A Particle Filtering Scheme for Processing Time Series Corrupted by Outliers (Journal Article) IEEE Transactions on Signal Processing, 60 (9), pp. 4611–4627, 2012, ISSN: 1053-587X. (Abstract | Links | BibTeX | Tags: Kalman filters, Mathematical model, nonlinear state space model, Outlier detection, prediction theory, predictive distribution, Probability density function, State-space methods, state-space models, statistical distributions, Target tracking, time serie processing, Vectors, Yttrium) @article{Maiz2012, title = {A Particle Filtering Scheme for Processing Time Series Corrupted by Outliers}, author = {Maiz, Cristina S. and Molanes-Lopez, Elisa M. and Miguez, Joaquin and Djuric, Petar M.}, url = {http://www.tsc.uc3m.es/~jmiguez/papers/P34_2012_A Particle Filtering Scheme for Processing Time Series Corrupted by Outliers.pdf http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6203606}, issn = {1053-587X}, year = {2012}, date = {2012-01-01}, journal = {IEEE Transactions on Signal Processing}, volume = {60}, number = {9}, pages = {4611--4627}, abstract = {The literature in engineering and statistics is abounding in techniques for detecting and properly processing anomalous observations in the data. Most of these techniques have been developed in the framework of static models and it is only in recent years that we have seen attempts that address the presence of outliers in nonlinear time series. For a target tracking problem described by a nonlinear state-space model, we propose the online detection of outliers by including an outlier detection step within the standard particle filtering algorithm. The outlier detection step is implemented by a test involving a statistic of the predictive distribution of the observations, such as a concentration measure or an extreme upper quantile. We also provide asymptotic results about the convergence of the particle approximations of the predictive distribution (and its statistics) and assess the performance of the resulting algorithms by computer simulations of target tracking problems with signal power observations.}, keywords = {Kalman filters, Mathematical model, nonlinear state space model, Outlier detection, prediction theory, predictive distribution, Probability density function, State-space methods, state-space models, statistical distributions, Target tracking, time serie processing, Vectors, Yttrium}, pubstate = {published}, tppubtype = {article} } The literature in engineering and statistics is abounding in techniques for detecting and properly processing anomalous observations in the data. Most of these techniques have been developed in the framework of static models and it is only in recent years that we have seen attempts that address the presence of outliers in nonlinear time series. For a target tracking problem described by a nonlinear state-space model, we propose the online detection of outliers by including an outlier detection step within the standard particle filtering algorithm. The outlier detection step is implemented by a test involving a statistic of the predictive distribution of the observations, such as a concentration measure or an extreme upper quantile. We also provide asymptotic results about the convergence of the particle approximations of the predictive distribution (and its statistics) and assess the performance of the resulting algorithms by computer simulations of target tracking problems with signal power observations. |

## Inproceedings |

Campo, Adria Tauste; Vazquez-Vilar, Gonzalo; i Fabregas, Albert Guillen; Koch, Tobias; Martinez, Alfonso Random Coding Bounds that Attain the Joint Source-Channel Exponent (Inproceeding) 2012 46th Annual Conference on Information Sciences and Systems (CISS), pp. 1–5, IEEE, Princeton, 2012, ISBN: 978-1-4673-3140-1. (Abstract | Links | BibTeX | Tags: code construction, combined source-channel coding, Csiszár error exponent, Ducts, error probability, error statistics, Gallager exponent, joint source-channel coding, joint source-channel exponent, random codes, random-coding upper bound, Yttrium) @inproceedings{Campo2012, title = {Random Coding Bounds that Attain the Joint Source-Channel Exponent}, author = {Campo, Adria Tauste and Vazquez-Vilar, Gonzalo and Fabregas, Albert Guillen i and Koch, Tobias and Martinez, Alfonso}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6310910}, isbn = {978-1-4673-3140-1}, year = {2012}, date = {2012-01-01}, booktitle = {2012 46th Annual Conference on Information Sciences and Systems (CISS)}, pages = {1--5}, publisher = {IEEE}, address = {Princeton}, abstract = {This paper presents a random-coding upper bound on the average error probability of joint source-channel coding that attains Csiszár's error exponent. The bound is based on a code construction for which source messages are assigned to disjoint subsets (classes), and codewords are generated according to a distribution that depends on the class of the source message. For a single class, the bound recovers Gallager's exponent; identifying the classes with source type classes, it recovers Csiszár's exponent. Moreover, it is shown that as a two appropriately designed classes are sufficient to attain Csiszár's exponent.}, keywords = {code construction, combined source-channel coding, Csiszár error exponent, Ducts, error probability, error statistics, Gallager exponent, joint source-channel coding, joint source-channel exponent, random codes, random-coding upper bound, Yttrium}, pubstate = {published}, tppubtype = {inproceedings} } This paper presents a random-coding upper bound on the average error probability of joint source-channel coding that attains Csiszár's error exponent. The bound is based on a code construction for which source messages are assigned to disjoint subsets (classes), and codewords are generated according to a distribution that depends on the class of the source message. For a single class, the bound recovers Gallager's exponent; identifying the classes with source type classes, it recovers Csiszár's exponent. Moreover, it is shown that as a two appropriately designed classes are sufficient to attain Csiszár's exponent. |