Applied and Computational Mathematics
Volume 6, Issue 4-1, July 2017, Pages: 16-38
Received: Sep. 11, 2015;
Accepted: Sep. 13, 2015;
Published: Jun. 17, 2016
Views 5540 Downloads 189
Loc Nguyen, Sunflower Soft Company, Ho Chi Minh city, Vietnam
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.
Tutorial on Hidden Markov Model, Applied and Computational Mathematics. Special Issue: Some Novel Algorithms for Global Optimization and Relevant Subjects.
Vol. 6, No. 4-1,
2017, pp. 16-38.
E. Fosler-Lussier, "Markov Models and Hidden Markov Models: A Brief Tutorial," 1998.
J. G. Schmolze, "An Introduction to Hidden Markov Models," 2001.
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.
L. Nguyen, "Mathematical Approaches to User Modeling," Journals Consortium, 2015.
B. Sean, "The Expectation Maximization Algorithm - A short tutorial," Sean Borman's Homepage, 2009.
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.
Y.-B. Jia, "Lagrange Multipliers," 2013.
S. Borman, "The Expectation Maximization Algorithm - A short tutorial," Sean Borman's Home Page, South Bend, Indiana, 2004.
D. Ramage, "Hidden Markov Models Fundamentals," 2007.
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].
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).