### 2016

Valera, Isabel; Ruiz, Francisco J R; Perez-Cruz, Fernando

Infinite Factorial Unbounded-State Hidden Markov Model Journal Article

In: 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}

}

Valera, Isabel; Ruiz, Francisco J R; Perez-Cruz, Fernando

Infinite Factorial Unbounded-State Hidden Markov Model Journal Article

In: 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}

}