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Minimal Realization Problems for Hidden Markov Models [article]

Qingqing Huang, Rong Ge, Sham Kakade, Munther Dahleh
2015 arXiv   pre-print
Consider a stationary discrete random process with alphabet size d, which is assumed to be the output process of an unknown stationary Hidden Markov Model (HMM).  ...  quasi-HMM realization and the minimal HMM realization can be efficiently computed based on the joint probabilities of all the length N strings, for N > 4 lceil log_d(k) rceil +1.  ...  Background Hidden Markov Models (HMMs) are widely used for describing discrete random processes, especially in the applications involving temporal pattern recognition such as speech and gesture recognition  ... 
arXiv:1411.3698v2 fatcat:ogx2gqzeh5hqblslxjdpvgxr2q

Minimal Realization Problems for Hidden Markov Models

Qingqing Huang, Rong Ge, Sham Kakade, Munther Dahleh
2016 IEEE Transactions on Signal Processing  
This paper addresses two fundamental problems in the context of Hidden Markov Models (HMMs).  ...  In the main theorem, we show that both the minimal quasi-HMM realization and the minimal HMM realization can be efficiently computed based on the joint probabilities of length N strings, for N in the order  ...  Background Hidden Markov Models (HMMs) are widely used for describing discrete random processes, especially in the applications involving temporal pattern recognition such as speech and gesture recognition  ... 
doi:10.1109/tsp.2015.2510969 fatcat:cll73mafwffuxl6ukpt556fi3a

Recursive Filtering Using Quasi-Realizations [chapter]

Bart Vanluyten, Jan C. Willems, Bart De Moor
2006 Lecture notes in control and information sciences  
The main point of this article is to illustrate that for this kind of filtering problem, it is not needed to have a positive hidden Markov realization of the joint process, but it suffices to have a quasi-realization  ...  In this paper we consider a finite state Markov chain with two outputs, an observed output and a to-be-estimated output, and derive a recursive estimator for the to-be-estimated output from an observed  ...  Our approach is to split up the problem in two steps. In the first step we model the given output probabilities by a joint quasi-hidden Markov model.  ... 
doi:10.1007/3-540-34774-7_47 fatcat:pmqv3clklbbo5ja7x2zzyu3qi4

Equivalence of state representations for hidden Markov models

Bart Vanluyten, Jan C. Willems, Bart De Moor
2008 Systems & control letters (Print)  
In this paper we consider the following problem for hidden Markov models: given a minimal hidden Markov model, derive conditions for another hidden Markov model to be equivalent and give a description  ...  Finally, we compare the results for hidden Markov models and linear Gaussian systems.  ...  Vincent Blondel (UCL, Belgium) for his helpful suggestions on the use of real algebraic geometry. Bart  ... 
doi:10.1016/j.sysconle.2007.10.004 fatcat:y4mxnkc62feixfnh5iop3gyuci

Balanced Truncation for a Class of Stochastic Jump Linear Systems and Model Reduction for Hidden Markov Models

Georgios Kotsalis, Alexandre Megretski, Munther A. Dahleh
2008 IEEE Transactions on Automatic Control  
A two step model reduction algorithm for hidden Markov models is also developed.  ...  He is also interested in model reduction problems for discrete-alphabet hidden markov models and universal learning approaches for systems with both continuous and discrete alphabets.  ...  ACKNOWLEDGMENT The authors would like to thank the reviewers for valuable comments and suggestions and V. Blondel for [14] .  ... 
doi:10.1109/tac.2008.2006931 fatcat:kxvip3rnxjbplezvx6cs2sgvdy

A Model Reduction Algorithm for Hidden Markov Models

Georgios Kotsalis, Alexandre Megretski, Munther A. Dahleh
2006 Proceedings of the 45th IEEE Conference on Decision and Control  
This paper presents a two step model reduction algorithm for discrete-time, finite state, finite alphabet Hidden Markov Models.  ...  Subsequently, the reduced order stochastic Jump Linear System is modified, so that it meets the constraints of an image of a Hidden Markov Model of the same order.  ...  Definitions and Review of a Result in 1) Hidden Markov Models: Hidden Markov Models can be defined in many equivalent ways.  ... 
doi:10.1109/cdc.2006.377011 dblp:conf/cdc/KotsalisMD06 fatcat:aordfvux45asdoum44uor7ftnu

Hidden Markov Random Fields and Swarm Particles: A Winning Combination in Image Segmentation

El-Hachemi Guerrout, Ramdane Mahiou, Samy Ait-Aoudia
2014 Information Engineering Research Institute procedia  
U(x), potentials sum on all cliques C yields Gibbs field energy function: ) ( ) ( x U x U C c c (2.7) Hidden Markov Random Field model The input image is considered as realization of a Markov Random  ...  In section 2, we provide some concepts of Markov Random Field model. Section 3 is devoted to Hidden Markov Field model and its use in image segmentation.  ... 
doi:10.1016/j.ieri.2014.09.065 fatcat:ioydmbrvvncqzlilwrwfl5oh6a

Unsupervised classification of radar images using hidden Markov chains and hidden Markov random fields

R. Fjortoft, Y. Delignon, W. Pieczynski, M. Sigelle, F. Tupin
2003 IEEE Transactions on Geoscience and Remote Sensing  
Hidden Markov chain models, applied to a Hilbert-Peano scan of the image, constitute a fast and robust alternative to hidden Markov random field models for spatial regularization of image analysis problems  ...  This paper describes unsupervised classification of radar images in the framework of hidden Markov models and generalized mixture estimation.  ...  One possible way to overcome this problem is to exploit spatial dependencies among different random variables via a hidden Markov model.  ... 
doi:10.1109/tgrs.2003.809940 fatcat:a4bib35cvza57daq7fz2jf5ax4

Comparative Analysis of Viterbi Training and Maximum Likelihood Estimation for HMMs [article]

Armen E. Allahverdyan, Aram Galstyan
2013 arXiv   pre-print
Furthermore, VT converges faster and results in sparser (simpler) models, thus realizing an automatic Occam's razor for HMM learning.  ...  We present an asymptotic analysis of Viterbi Training (VT) and contrast it with a more conventional Maximum Likelihood (ML) approach to parameter estimation in Hidden Markov Models.  ...  Figure 1 : The hidden Markov process (21) (22) for ǫ = 0. Gray circles and arrows indicate on the realization and transitions of the internal Markov process; see (21) .  ... 
arXiv:1312.4551v1 fatcat:ivxe6hg73jaktgeogiva5logbe

Unsupervised restoration of hidden nonstationary Markov chains using evidential priors

P. Lanchantin, W. Pieczynski
2005 IEEE Transactions on Signal Processing  
The novelty of this paper is to offer a more appropriate model for hidden nonstationary Markov chains, via the theory of evidence.  ...  This paper addresses the problem of unsupervised Bayesian hidden Markov chain restoration.  ...  INTRODUCTION T HE hidden Markov chain (HMC) model is widely used for various problems, including signal and image processing, economical prediction, and health sciences.  ... 
doi:10.1109/tsp.2005.851131 fatcat:cgp2spvonnfjlnzdmt7agivowa

Hidden Gibbs random fields model selection using Block Likelihood Information Criterion

Julien Stoehr, Jean-Michel Marin, Pierre Pudlo
2016 Stat  
We study the performances of BLIC for those questions.  ...  Furthermore, such unobserved fields cannot be integrated out and the likelihood evaluztion is a doubly intractable problem.  ...  (a) BIC MF-like , BIC GBF and BLIC MF-like 2×2 values for one realization of a first order hidden Potts model HPM(G , θ, 4).  ... 
doi:10.1002/sta4.112 fatcat:whvrafcn2nd5fc4dxgw2lyhnua

Inference, Prediction, and Entropy-Rate Estimation of Continuous-time, Discrete-event Processes [article]

S. E. Marzen, J. P. Crutchfield
2020 arXiv   pre-print
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground.  ...  Here, we provide new methods for inferring, predicting, and estimating them.  ...  A minimal unifilar hidden semi-Markov model has two key properties: • Unifilarity: if the current hidden state and next emission are known, then the next hidden state is determined; and • Minimality: minimal  ... 
arXiv:2005.03750v1 fatcat:fwxzmon3zzep7ojzm3bcjmztsm

Hidden fuzzy Markov chain model with K discrete classes

Ahmed Gamal-Eldin, Fabien Salzenstein, Christophe Collet
2010 10th International Conference on Information Science, Signal Processing and their Applications (ISSPA 2010)  
This paper deals with a new unsupervised fuzzy Bayesian segmentation method based on the hidden Markov chain model, in order to separate continuous from discrete components in the hidden data.  ...  For a given observation, the hidden variable owns a density according to a measure containing Dirac and Lebesgue components. We have performed our approach in the multispectral context.  ...  The authors would like to thank the laboratory INRIA Sophia-Antipolis (France) for the financial support.  ... 
doi:10.1109/isspa.2010.5605506 dblp:conf/isspa/Gamal-EldinSC10 fatcat:kosm3tjuhjcpdflt6evuvakjti

Lumpable hidden Markov models-model reduction and reduced complexity filtering

L.B. White, R. Mahony, G.D. Brushe
2000 IEEE Transactions on Automatic Control  
For a particular class of hidden Markov models (HMMs), namely finite output alphabet models, conditions for lumpability of all HMPs representable by a specified HMM are given.  ...  This paper is concerned with filtering of hidden Markov processes (HMPs) which possess (or approximately possess) the property of lumpability.  ...  Anderson for helpful comments. They also thank the associate editor and anonymous referees for helpful suggestions.  ... 
doi:10.1109/9.895565 fatcat:wujmxrrdtjcmvn2puelqp5e7rq

A generalized risk approach to path inference based on hidden Markov models [article]

Jüri Lember, Alexey A. Koloydenko
2013 arXiv   pre-print
Motivated by the unceasing interest in hidden Markov models (HMMs), this paper re-examines hidden path inference in these models, using primarily a risk-based framework.  ...  Furthermore, simple modifications of the classical criteria for hidden path recognition are shown to lead to a new class of decoders.  ...  inference about the hidden realizations as well as model parameters (if any).  ... 
arXiv:1007.3622v4 fatcat:l72q6cdgg5gm5pq6glh7j42d2e
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