Second-Order Belief Hidden Markov Models

Hidden Markov Models (HMMs) are learning methods for pattern recognition. The probabilistic HMMs have been one of the most used techniques based on the Bayesian model. First-order probabilistic HMMs were adapted to the theory of belief functions such that Bayesian probabilities were replaced with mass functions. In this paper, we present a second-order Hidden Markov Model using belief functions. Previous works in belief HMMs have been focused on the first-order HMMs. We extend them to the second-order model.

[1]  Noureddine Zerhouni,et al.  Time-Sliced Temporal Evidential Networks: The case of Evidential HMM with application to dynamical system analysis , 2011, 2011 IEEE Conference on Prognostics and Health Management.

[2]  James H. Martin,et al.  Speech and language processing: an introduction to natural language processing, computational linguistics, and speech recognition, 2nd Edition , 2000, Prentice Hall series in artificial intelligence.

[3]  W. Pieczynski,et al.  An evidential Markovian model for data fusion and unsupervised image classification , 2000, Proceedings of the Third International Conference on Information Fusion.

[4]  Thierry Denoeux,et al.  Partially-Hidden Markov Models , 2012, Belief Functions.

[5]  Thierry Denoeux,et al.  Constructing consonant belief functions from sample data using confidence sets of pignistic probabilities , 2008, Int. J. Approx. Reason..

[6]  Emmanuel Monfrini,et al.  Dempster–Shafer fusion of multisensor signals in nonstationary Markovian context , 2012, EURASIP Journal on Advances in Signal Processing.

[7]  Alessandro Saffiotti,et al.  The Transferable Belief Model , 1991, ECSQARU.

[8]  Thorsten Brants,et al.  TnT – A Statistical Part-of-Speech Tagger , 2000, ANLP.

[9]  Jorma Rissanen,et al.  Partially hidden Markov models , 1996, IEEE Trans. Inf. Theory.

[10]  Véronique Cherfaoui,et al.  Object-level fusion and confidence management in a multi-sensor pedestrian tracking system , 2008 .

[11]  Julian M. Kupiec,et al.  Robust part-of-speech tagging using a hidden Markov model , 1992 .

[12]  Henri Prade,et al.  Representation and combination of uncertainty with belief functions and possibility measures , 1988, Comput. Intell..

[13]  Arnaud Martin,et al.  Belief Hidden Markov Model for speech recognition , 2013, 2013 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO).

[14]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[15]  Emmanuel Ramasso,et al.  Reconnaissance de séquences d'états par le Modèle des Croyances Transférables. Application à l'analyse de vidéos d'athlétisme. (State sequence recognition based on the Transferable Belief Model. Application to athletics videos analysis) , 2007 .

[16]  Lee-Min Lee,et al.  A Study on High-Order Hidden Markov Models and Applications to Speech Recognition , 2006, IEA/AIE.

[17]  Philippe Smets,et al.  Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem , 1993, Int. J. Approx. Reason..

[18]  J. J. Sudano.  Inverse pignistic probability transforms , 2002, Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997).

[19]  Pierre Lanchantin,et al.  Unsupervised restoration of hidden nonstationary Markov chains using evidential priors , 2005, IEEE Transactions on Signal Processing.

[20]  Mary P. Harper,et al.  A Second-Order Hidden Markov Model for Part-of-Speech Tagging , 1999, ACL.

[21]  Jian Su,et al.  Named Entity Recognition using an HMM-based Chunk Tagger , 2002, ACL.

[22]  Biing-Hwang Juang,et al.  Hidden Markov Models for Speech Recognition , 1991 .

[23]  Hélène Soubaras.  On Evidential Markov Chains , 2010 .

[24]  Philippe Smets,et al.  Analyzing the combination of conflicting belief functions , 2007, Inf. Fusion.

[25]  Thierry Denoeux,et al.  Making Use of Partial Knowledge About Hidden States in HMMs: An Approach Based on Belief Functions , 2014, IEEE Transactions on Fuzzy Systems.

[26]  Wojciech Pieczynski,et al.  Multisensor triplet Markov chains and theory of evidence , 2007, Int. J. Approx. Reason..

[27]  Emmanuel Ramasso,et al.  Contribution of belief functions to hidden markov models with an application to fault diagnosis , 2009, 2009 IEEE International Workshop on Machine Learning for Signal Processing.

[28]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[29]  R. Yager.  On the dempster-shafer framework and new combination rules , 1987, Inf. Sci..

[30]  Mark Johnson,et al.  Why Doesn’t EM Find Good HMM POS-Taggers? , 2007, EMNLP.

[31]  Virginia Teller.  Review of Speech and language processing: an introduction to natural language processing, computational linguistics, and speech recognition by Daniel Jurafsky and James H. Martin. Prentice Hall 2000. , 2000 .