## 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. |

## 2015 |

Ramírez, David; Schreier, Peter J; Via, Javier; Santamaria, Ignacio; Scharf, Louis L Detection of Multivariate Cyclostationarity Journal Article IEEE Transactions on Signal Processing, 63 (20), pp. 5395–5408, 2015, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: ad hoc function, asymptotic GLRT, asymptotic LMPIT, block circulant, block-Toeplitz structure, Correlation, covariance matrices, Covariance matrix, covariance structure, cycle period, cyclic spectrum, Cyclostationarity, Detectors, Frequency-domain analysis, generalized likelihood ratio test, generalized likelihood ratio test (GLRT), hypothesis testing problem, locally most powerful invariant test, locally most powerful invariant test (LMPIT), Loe{&amp;amp;}{#}x0300, maximum likelihood estimation, multivariate cyclostationarity detection, power spectral density, random processes, s theorem, scalar valued CS time series, signal detection, spectral analysis, statistical testing, Testing, Time series, Time series analysis, Toeplitz matrices, Toeplitz matrix, ve spectrum, vector valued random process cyclostationary, vector valued WSS time series, wide sense stationary, Wijsman theorem, Wijsman{&amp;amp;}{#}x2019 @article{Ramirez2015, title = {Detection of Multivariate Cyclostationarity}, author = {David Ramírez and Peter J Schreier and Javier Via and Ignacio Santamaria and Louis L Scharf}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7134806}, doi = {10.1109/TSP.2015.2450201}, issn = {1053-587X}, year = {2015}, date = {2015-10-01}, journal = {IEEE Transactions on Signal Processing}, volume = {63}, number = {20}, pages = {5395--5408}, publisher = {IEEE}, abstract = {This paper derives an asymptotic generalized likelihood ratio test (GLRT) and an asymptotic locally most powerful invariant test (LMPIT) for two hypothesis testing problems: 1) Is a vector-valued random process cyclostationary (CS) or is it wide-sense stationary (WSS)? 2) Is a vector-valued random process CS or is it nonstationary? Our approach uses the relationship between a scalar-valued CS time series and a vector-valued WSS time series for which the knowledge of the cycle period is required. This relationship allows us to formulate the problem as a test for the covariance structure of the observations. The covariance matrix of the observations has a block-Toeplitz structure for CS and WSS processes. By considering the asymptotic case where the covariance matrix becomes block-circulant we are able to derive its maximum likelihood (ML) estimate and thus an asymptotic GLRT. Moreover, using Wijsman's theorem, we also obtain an asymptotic LMPIT. These detectors may be expressed in terms of the Loève spectrum, the cyclic spectrum, and the power spectral density, establishing how to fuse the information in these spectra for an asymptotic GLRT and LMPIT. This goes beyond the state-of-the-art, where it is common practice to build detectors of cyclostationarity from ad-hoc functions of these spectra.}, keywords = {ad hoc function, asymptotic GLRT, asymptotic LMPIT, block circulant, block-Toeplitz structure, Correlation, covariance matrices, Covariance matrix, covariance structure, cycle period, cyclic spectrum, Cyclostationarity, Detectors, Frequency-domain analysis, generalized likelihood ratio test, generalized likelihood ratio test (GLRT), hypothesis testing problem, locally most powerful invariant test, locally most powerful invariant test (LMPIT), Loe{&amp;amp;}{#}x0300, maximum likelihood estimation, multivariate cyclostationarity detection, power spectral density, random processes, s theorem, scalar valued CS time series, signal detection, spectral analysis, statistical testing, Testing, Time series, Time series analysis, Toeplitz matrices, Toeplitz matrix, ve spectrum, vector valued random process cyclostationary, vector valued WSS time series, wide sense stationary, Wijsman theorem, Wijsman{&amp;amp;}{#}x2019}, pubstate = {published}, tppubtype = {article} } This paper derives an asymptotic generalized likelihood ratio test (GLRT) and an asymptotic locally most powerful invariant test (LMPIT) for two hypothesis testing problems: 1) Is a vector-valued random process cyclostationary (CS) or is it wide-sense stationary (WSS)? 2) Is a vector-valued random process CS or is it nonstationary? Our approach uses the relationship between a scalar-valued CS time series and a vector-valued WSS time series for which the knowledge of the cycle period is required. This relationship allows us to formulate the problem as a test for the covariance structure of the observations. The covariance matrix of the observations has a block-Toeplitz structure for CS and WSS processes. By considering the asymptotic case where the covariance matrix becomes block-circulant we are able to derive its maximum likelihood (ML) estimate and thus an asymptotic GLRT. Moreover, using Wijsman's theorem, we also obtain an asymptotic LMPIT. These detectors may be expressed in terms of the Loève spectrum, the cyclic spectrum, and the power spectral density, establishing how to fuse the information in these spectra for an asymptotic GLRT and LMPIT. This goes beyond the state-of-the-art, where it is common practice to build detectors of cyclostationarity from ad-hoc functions of these spectra. |