Abstract
We propose a novel approach to learn the structure of Partially Observable Markov Models (POMMs) and to estimate jointly their parameters. POMMs are graphical models equivalent to Hidden Markov Models (HMMs). The model structure is built to support the First Passage Times (FPT) dynamics observed in the training sample. We argue that the FPT in POMMs are closely related to the model structure. Starting from a standard Markov chain, states are iteratively added to the model. A novel algorithm POMMPHit is proposed to estimate the POMM transition probabilities to fit the sample FPT dynamics. The transitions with the lowest expected passage times are trimmed off from the model. Practical evaluations on artificially generated data and on DNA sequence modeling show the benefits over Bayesian model induction or EM estimation of ergodic models with transition trimming.
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Callut, J., Dupont, P.: Inducing hidden markov models to model long-term dependencies. In: Gama, J., Camacho, R., Brazdil, P.B., Jorge, A.M., Torgo, L. (eds.) ECML 2005. LNCS (LNAI), vol. 3720, pp. 513–521. Springer, Heidelberg (2005)
Durbin, R., Eddy, S., Krogh, A., Mitchison, G.: Biological sequence analysis. Cambridge University Press, Cambridge (1998)
Freitag, D., McCallum, A.: Information extraction with HMM structures learned by stochastic optimization. In: Proc. of the Seventeenth National Conference on Artificial Intelligence, AAAI, pp. 584–589 (2000)
Kemeny, J.G., Snell, J.L.: Finite Markov Chains. Springer, Heidelberg (1983)
Latouche, G., Ramaswami, V.: Introduction to Matrix Analytic Methods in Stochastic Modeling. Society for Industrial & Applied Mathematics, U.S. (1999)
Li, J., Wang, J., Zhao, Y., Yang, Z.: Self-adaptive design of hidden markov models. Pattern Recogn. Lett. 25(2), 197–210 (2004)
Lin, J.: Divergence measures based on the shannon entropy. IEEE Trans. Information Theory 37, 145–151 (1991)
Ostendorf, M., Singer, H.: HMM topology design using maximum likelihood successive state splitting. Computer Speech and Language 11, 17–41 (1997)
Rabiner, L., Juang, B.-H.: Fundamentals of Speech Recognition. Prentice-Hall, Englewood Cliffs (1993)
Stolcke, A.: Bayesian Learning of Probabilistic Language Models. Ph. D. dissertation, University of California (1994)
Zhu, H., Wang, J., Yang, Z., Song, Y.: A method to design standard hmms with desired length distribution for biological sequence analysis. In: Bücher, P., Moret, B.M.E. (eds.) WABI 2006. LNCS (LNBI), vol. 4175, pp. 24–31. Springer, Heidelberg (2006)
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Callut, J., Dupont, P. (2007). Learning Partially Observable Markov Models from First Passage Times. In: Kok, J.N., Koronacki, J., Mantaras, R.L.d., Matwin, S., Mladenič, D., Skowron, A. (eds) Machine Learning: ECML 2007. ECML 2007. Lecture Notes in Computer Science(), vol 4701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74958-5_12
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DOI: https://doi.org/10.1007/978-3-540-74958-5_12
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