Applied and Computational Mathematics

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Tutorial on Hidden Markov Model

Received: 11 September 2015    Accepted: 13 September 2015    Published: 17 June 2016
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Abstract

Hidden Markov model (HMM) is a powerful mathematical tool for prediction and recognition. Many computer software products implement HMM and hide its complexity, which assist scientists to use HMM for applied researches. However comprehending HMM in order to take advantages of its strong points requires a lot of efforts. This report is a tutorial on HMM with full of mathematical proofs and example, which help researchers to understand it by the fastest way from theory to practice. The report focuses on three common problems of HMM such as evaluation problem, uncovering problem, and learning problem, in which learning problem with support of optimization theory is the main subject.

DOI 10.11648/j.acm.s.2017060401.12
Published in Applied and Computational Mathematics (Volume 6, Issue 4-1, July 2017)

This article belongs to the Special Issue Some Novel Algorithms for Global Optimization and Relevant Subjects

Page(s) 16-38
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Hidden Markov Model, Optimization, Evaluation Problem, Uncovering Problem, Learning Problem

References
[1] E. Fosler-Lussier, "Markov Models and Hidden Markov Models: A Brief Tutorial," 1998.
[2] J. G. Schmolze, "An Introduction to Hidden Markov Models," 2001.
[3] L. R. Rabiner, "A tutorial on hidden Markov models and selected applications in speech recognition," Proceedings of the IEEE, vol. 77, no. 2, pp. 257-286, 1989.
[4] L. Nguyen, "Mathematical Approaches to User Modeling," Journals Consortium, 2015.
[5] B. Sean, "The Expectation Maximization Algorithm - A short tutorial," Sean Borman's Homepage, 2009.
[6] A. P. Dempster, N. M. Laird and D. B. Rubin, "Maximum Likelihood from Incomplete Data via the EM Algorithm," Journal of the Royal Statistical Society, Series B (Methodological), vol. 39, no. 1, pp. 1-38, 1977.
[7] Y.-B. Jia, "Lagrange Multipliers," 2013.
[8] S. Borman, "The Expectation Maximization Algorithm - A short tutorial," Sean Borman's Home Page, South Bend, Indiana, 2004.
[9] D. Ramage, "Hidden Markov Models Fundamentals," 2007.
[10] Wikipedia, "Karush–Kuhn–Tucker conditions," Wikimedia Foundation, 4 August 2014. [Online]. Available: http://en.wikipedia.org/wiki/Karush–Kuhn–Tucker_conditions. [Accessed 16 November 2014].
[11] S. Boyd and L. Vandenberghe, Convex Optimization, New York, NY: Cambridge University Press, 2009, p. 716.G. Eason, B. Noble, and I. N. Sneddon, “On certain integrals of Lipschitz-Hankel type involving products of Bessel functions,” Phil. Trans. Roy. Soc. London, vol. A247, pp. 529–551, April 1955. (references).
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    Loc Nguyen. (2016). Tutorial on Hidden Markov Model. Applied and Computational Mathematics, 6(4-1), 16-38. https://doi.org/10.11648/j.acm.s.2017060401.12

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    Loc Nguyen. Tutorial on Hidden Markov Model. Appl. Comput. Math. 2016, 6(4-1), 16-38. doi: 10.11648/j.acm.s.2017060401.12

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    Loc Nguyen. Tutorial on Hidden Markov Model. Appl Comput Math. 2016;6(4-1):16-38. doi: 10.11648/j.acm.s.2017060401.12

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  • @article{10.11648/j.acm.s.2017060401.12,
      author = {Loc Nguyen},
      title = {Tutorial on Hidden Markov Model},
      journal = {Applied and Computational Mathematics},
      volume = {6},
      number = {4-1},
      pages = {16-38},
      doi = {10.11648/j.acm.s.2017060401.12},
      url = {https://doi.org/10.11648/j.acm.s.2017060401.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.s.2017060401.12},
      abstract = {Hidden Markov model (HMM) is a powerful mathematical tool for prediction and recognition. Many computer software products implement HMM and hide its complexity, which assist scientists to use HMM for applied researches. However comprehending HMM in order to take advantages of its strong points requires a lot of efforts. This report is a tutorial on HMM with full of mathematical proofs and example, which help researchers to understand it by the fastest way from theory to practice. The report focuses on three common problems of HMM such as evaluation problem, uncovering problem, and learning problem, in which learning problem with support of optimization theory is the main subject.},
     year = {2016}
    }
    

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