## 2016 |

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&amp;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 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&amp;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. |

## 2013 |

Alvarez, Mauricio; Luengo, David; Lawrence, Neil D Linear Latent Force Models Using Gaussian Processes Journal Article IEEE Trans. Pattern Anal. Mach. Intell., 35 (11), pp. 2693–2705, 2013. Abstract | Links | BibTeX | Tags: Analytical models, Computational modeling, Data models, Differential equations, Force, Gaussian processes, Mathematical mode @article{Alvarez2013, title = {Linear Latent Force Models Using Gaussian Processes}, author = {Mauricio Alvarez and David Luengo and Neil D Lawrence}, url = {http://dblp.uni-trier.de/db/journals/pami/pami35.html#AlvarezLL13 http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6514873}, year = {2013}, date = {2013-01-01}, journal = {IEEE Trans. Pattern Anal. Mach. Intell.}, volume = {35}, number = {11}, pages = {2693--2705}, abstract = {Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics.}, keywords = {Analytical models, Computational modeling, Data models, Differential equations, Force, Gaussian processes, Mathematical mode}, pubstate = {published}, tppubtype = {article} } Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics. |

## 2010 |

Achutegui, Katrin; Rodas, Javier; Escudero, Carlos J; Miguez, Joaquin A Model-Switching Sequential Monte Carlo Algorithm for Indoor Tracking with Experimental RSS Data Inproceedings 2010 International Conference on Indoor Positioning and Indoor Navigation, pp. 1–8, IEEE, Zurich, 2010, ISBN: 978-1-4244-5862-2. Abstract | Links | BibTeX | Tags: Approximation methods, Computational modeling, Data models, generalized IMM system, GIMM approach, indoor radio, Indoor tracking, Kalman filters, maneuvering target motion, Mathematical model, model switching sequential Monte Carlo algorithm, Monte Carlo methods, multipath propagation, multiple model interaction, propagation environment, radio receivers, radio tracking, radio transmitters, random processes, Rao-Blackwellized sequential Monte Carlo tracking, received signal strength, RSS data, sensors, state space model, target position dependent data, transmitter-to-receiver distance, wireless technology @inproceedings{Achutegui2010, title = {A Model-Switching Sequential Monte Carlo Algorithm for Indoor Tracking with Experimental RSS Data}, author = {Katrin Achutegui and Javier Rodas and Carlos J Escudero and Joaquin Miguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5648053}, isbn = {978-1-4244-5862-2}, year = {2010}, date = {2010-01-01}, booktitle = {2010 International Conference on Indoor Positioning and Indoor Navigation}, pages = {1--8}, publisher = {IEEE}, address = {Zurich}, abstract = {In this paper we address the problem of indoor tracking using received signal strength (RSS) as position-dependent data. This type of measurements are very appealing because they can be easily obtained with a variety of (inexpensive) wireless technologies. However, the extraction of accurate location information from RSS in indoor scenarios is not an easy task. Due to the multipath propagation, it is hard to adequately model the correspondence between the received power and the transmitter-to-receiver distance. For that reason, we propose the use of a compound model that combines several sub-models, whose parameters are adjusted to different propagation environments. This methodology, called Interacting Multiple Models (IMM), has been used in the past either for modeling the motion of maneuvering targets or the relationship between the target position and the observations. Here, we extend its application to handle both types of uncertainty simultaneously and we refer to the resulting state-space model as a generalized IMM (GIMM) system. The flexibility of the GIMM approach is attained at the expense of an increase in the number of random processes that must be accurately tracked. To overcome this difficulty, we introduce a Rao-Blackwellized sequential Monte Carlo tracking algorithm that exhibits good performance both with synthetic and experimental data.}, keywords = {Approximation methods, Computational modeling, Data models, generalized IMM system, GIMM approach, indoor radio, Indoor tracking, Kalman filters, maneuvering target motion, Mathematical model, model switching sequential Monte Carlo algorithm, Monte Carlo methods, multipath propagation, multiple model interaction, propagation environment, radio receivers, radio tracking, radio transmitters, random processes, Rao-Blackwellized sequential Monte Carlo tracking, received signal strength, RSS data, sensors, state space model, target position dependent data, transmitter-to-receiver distance, wireless technology}, pubstate = {published}, tppubtype = {inproceedings} } In this paper we address the problem of indoor tracking using received signal strength (RSS) as position-dependent data. This type of measurements are very appealing because they can be easily obtained with a variety of (inexpensive) wireless technologies. However, the extraction of accurate location information from RSS in indoor scenarios is not an easy task. Due to the multipath propagation, it is hard to adequately model the correspondence between the received power and the transmitter-to-receiver distance. For that reason, we propose the use of a compound model that combines several sub-models, whose parameters are adjusted to different propagation environments. This methodology, called Interacting Multiple Models (IMM), has been used in the past either for modeling the motion of maneuvering targets or the relationship between the target position and the observations. Here, we extend its application to handle both types of uncertainty simultaneously and we refer to the resulting state-space model as a generalized IMM (GIMM) system. The flexibility of the GIMM approach is attained at the expense of an increase in the number of random processes that must be accurately tracked. To overcome this difficulty, we introduce a Rao-Blackwellized sequential Monte Carlo tracking algorithm that exhibits good performance both with synthetic and experimental data. |