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Hidden Markov Models with mixtures as emission distributions

Stevenn Volant, Caroline Bérard, Marie-Laure Martin-Magniette, Stéphane Robin
2013 Statistics and computing  
In this paper, a semiparametric modeling where the emission distributions are a mixture of parametric distributions is proposed to get a higher flexibility.  ...  In unsupervised classification, Hidden Markov Models (HMM) are used to account for a neighborhood structure between observations.  ...  using mixture as emission distributions (Li, 2005 , Baudry et al., 2008 .  ... 
doi:10.1007/s11222-013-9383-7 fatcat:3xp2q3ymzjgchbyyshifi6tyvm

Hidden Markov Models with mixtures as emission distributions [article]

Stevenn Volant, Caroline Bérard, Marie-Laure Martin-Magniette and Stéphane Robin
2012 arXiv   pre-print
In this paper, a semiparametric modeling where the emission distributions are a mixture of parametric distributions is proposed to get a higher flexibility.  ...  In unsupervised classification, Hidden Markov Models (HMM) are used to account for a neighborhood structure between observations.  ...  using mixture as emission distributions (Li, 2005 , Baudry et al., 2008 .  ... 
arXiv:1206.5102v1 fatcat:j7s5qpdpljd43kb42qooxsalr4

Finite state space non parametric Hidden Markov Models are in general identifiable [article]

Elisabeth Gassiat and Alice Cleynen and Stéphane Robin
2013 arXiv   pre-print
In this paper, we prove that finite state space non parametric hidden Markov models are identifiable as soon as the transition matrix of the latent Markov chain has full rank and the emission probability  ...  distributions are linearly independent.  ...  The emission distribution µ j is defined as µ j = ψ j φ . (4) A simple mixture model (i.e. when the hidden variable X i are iid) with such emission distribution is not identifiable (see [2] ).  ... 
arXiv:1306.4657v1 fatcat:b4s2h4dr4jdsro6giirvvxasim

MRHMMs: Multivariate Regression Hidden Markov Models and the variantS

Yeonok Lee, Debashis Ghosh, Ross C. Hardison, Yu Zhang
2014 Computer applications in the biosciences : CABIOS  
First, MRHMMs provides a diverse set of emission probability structures, including mixture of multivariate normal distributions and (logistic) regression models.  ...  Hidden Markov models (HMMs) are flexible and widely used in scientific studies.  ...  MATERIALS AND METHODS An HMM can be viewed as a mixture model in which the latent (hidden) state has the Markov property.  ... 
doi:10.1093/bioinformatics/btu070 pmid:24558116 pmcid:PMC4058941 fatcat:cpeajlfryje7rn5vdtxqwkz4ly

Hhsmm: An R package for hidden hybrid Markov/semi-Markov models [article]

Morteza Amini, Afarin Bayat, Reza Salehian
2022 arXiv   pre-print
The hhsmm also includes Markov/semi-Markov switching regression model as well as the auto-regressive HHSMM, the nonparametric estimation of the emission distribution using penalized B-splines, prediction  ...  This paper introduces the hhsmm R package, which involves functions for initializing, fitting, and predication of hidden hybrid Markov/semi-Markov models.  ...  Examples of hidden hybrid Markov/semi-Markov models Some examples of HHSMM models are as follows: • Models with macro-states: The macro-states are series or parallel networks of states with common emission  ... 
arXiv:2109.12489v6 fatcat:4faxrk7konaktp6nib4vzfc5iy

Effects of Frequency-Based Inter-frame Dependencies on Automatic Speech Recognition [chapter]

Ludovic Trottier, Brahim Chaib-draa, Philippe Giguère
2014 Lecture Notes in Computer Science  
Model A Hidden Markov Model with a Matrix Normal Mixture Model as the emission density was designed. Motivations High-dimensional features.  ...  Motivations Signal processing theories show that the rate at which information changes in signals is proportional to frequency. 2 Model A Hidden Markov Model with a Matrix Normal Mixture Model as the emission  ...  Model A Hidden Markov Model with a Matrix Normal Mixture Model as the emission density was designed.  ... 
doi:10.1007/978-3-319-06483-3_38 fatcat:rfknz3lchbbojlfaapn6gfol3q

Implementing spectral methods for hidden Markov models with real-valued emissions [article]

Carl Mattfeld
2014 arXiv   pre-print
Hidden Markov models (HMMs) are widely used statistical models for modeling sequential data. The parameter estimation for HMMs from time series data is an important learning problem.  ...  Using experiments with synthetic data, the algorithms are compared with each other.  ...  For the initial state h 1 , the initial state distribution is denoted by the vector π ∈ R k , with π j = Pr [h 1 = j] . (1.6) Emissions The emissions of a hidden Markov model can be parameterized by  ... 
arXiv:1404.7472v1 fatcat:jlwnuj67vfer5g2b6ecvdd3xgm

A General Strategy for Hidden Markov Chain Parameterisation in Composite Feature-Spaces [chapter]

David Windridge, Richard Bowden, Josef Kittler
2004 Lecture Notes in Computer Science  
A general technique for the construction of hidden Markov models (HMMs) from multiple-variable time-series observations in noisy experimental environments is set out.  ...  In retaining correlation information between features, the method is potentially far more general than Gaussian mixture model HMM parameterisation methods such as Baum-Welch re-estimation, to which we  ...  Most importantly, this mapping will be of an essentially stochastic nature, as required by the relation of hidden and observed states in hidden Markov modelling [cf eg. 2].  ... 
doi:10.1007/978-3-540-27868-9_118 fatcat:k47glovk2ndx5pj5agisdil45m

Bayesian non-parametric hidden Markov models with applications in genomics

C. Yau, O. Papaspiliopoulos, G. O. Roberts, C. Holmes
2010 Journal of The Royal Statistical Society Series B-statistical Methodology  
Analysing various real data sets we find significantly more accurate inference compared with state of the art hidden Markov models which use finite mixture emission distributions.  ...  We propose a flexible non-parametric specification of the emission distribution in hidden Markov models and we introduce a novel methodology for carrying out the computations.  ...  emission distribution as a finite mixture model.  ... 
doi:10.1111/j.1467-9868.2010.00756.x pmid:21687778 pmcid:PMC3116623 fatcat:5xdtn4m2ifdbpn35wt3ey7dhlm

Inference in finite state space non parametric Hidden Markov Models and applications

E. Gassiat, A. Cleynen, S. Robin
2015 Statistics and computing  
Hidden Markov models (HMMs) are intensively used in various fields to model and classify data observed along a line (e.g. time).  ...  In this paper, we prove that finite state space non parametric HMMs are identifiable as soon as the transition matrix of the latent Markov chain has full rank and the emission probability distributions  ...  The emission distribution μ j is defined as μ j = ψ j φ . (4) A simple mixture model (i.e. when the hidden variable X i are iid) with such emission distribution is not identifiable (see Baudry et al.  ... 
doi:10.1007/s11222-014-9523-8 fatcat:2i4vujmg4rfajoukiep4odedhi

Mixture Hidden Markov Models for Sequence Data: The seqHMM Package in R

Satu Helske, Jouni Helske
2019 Journal of Statistical Software  
Extending to mixture hidden Markov models (MHMMs) allows clustering data into homogeneous subsets, with or without external covariates.  ...  Also other restricted variants of the MHMM can be fitted, e.g., latent class models, Markov models, mixture Markov models, or even ordinary multinomial regression models with suitable parameterization  ...  Acknowledgments We also wish to thank Mervi Eerola and Jukka Nyblom as well as the editor and two anonymous referees for their helpful comments and suggestions.  ... 
doi:10.18637/jss.v088.i03 fatcat:nsttmgyslncq3cfquh3xxslv3u

A New Generative Feature Set Based on Entropy Distance for Discriminative Classification [chapter]

Alessandro Perina, Marco Cristani, Umberto Castellani, Vittorio Murino
2009 Lecture Notes in Computer Science  
The proposed score space is presented for hidden Markov models and mixture of gaussian and is experimentally validated on standard benchmark datasets; moreover it can be applied to any generative model  ...  In this way, both uncertainty in the generative model learning step and "local" compliance of data observations with respect to the generative process can be represented.  ...  On the right the graphical model that represent the mixture of Gaussians which can be viewed as a single slice of an hidden Markov model with gaussian emission. 1.  ... 
doi:10.1007/978-3-642-04146-4_23 fatcat:a24h332tarhufmfdcoqtkjq4xq

Analyzing Single-Molecule Time Series via Nonparametric Bayesian Inference

Keegan E. Hines, John R. Bankston, Richard W. Aldrich
2015 Biophysical Journal  
We demonstrate these methods with applications to several diverse settings in single-molecule biophysics.  ...  The interpretation of single-molecule time series has often been rooted in statistical mechanics and the theory of Markov processes.  ...  In this infinite aggregated Markov model (iAMM) (35), we imagine that the hidden states appear as aggregated into one of A distinct emission distributions such that A < K.  ... 
doi:10.1016/j.bpj.2014.12.016 pmid:25650922 pmcid:PMC4317543 fatcat:jzqb2qglurfehfw34qbyo5g2qm

A Hybrid Hidden Markov Model for Pipeline Leakage Detection

Mingchi Zhang, Xuemin Chen, Wei Li
2021 Applied Sciences  
Two comparative studies based on different numbers of states using Gaussian mixture model-hidden Markov model (GMM-HMM) and DNN-HMM are performed.  ...  A long pipeline is divided into several sections and the leakage occurs in different section that is defined as different state of hidden Markov model (HMM).  ...  Hidden Markov Model The hidden Markov model is a probabilistic graphical model in which the unobservable ("hidden") system state sequence is modeled by Markov chain, and hidden states can be indirectly  ... 
doi:10.3390/app11073138 fatcat:7bzkrqfqunfvtdyihg4aw3gxna

Abnormal Behavior Recognition Using Self-Adaptive Hidden Markov Models [chapter]

Jun Yin, Yan Meng
2009 Lecture Notes in Computer Science  
A self-adaptive Hidden Markov Model (SA-HMM) based framework is proposed for behavior recognition in this paper.  ...  During the training stage, the state transition and output probabilities of HMMs can be optimized through the Gaussian Mixture Models (GMMs) so the generated symbols can match the observed image features  ...  Hidden Markov Models A Hidden Markov Model (HMM) [11] is a statistical model in which the system being modeled is assumed to be a Markov process with unknown parameters, and the challenge is to determine  ... 
doi:10.1007/978-3-642-02611-9_34 fatcat:mlhlbnmqwzh65icyyqg5sqqz7u
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