Métodos de inferencia estadística para entrenamiento de modelos ocultos de Markov

Ricardo Antonio Mendoza León


Este documento presenta una revisión general de las diferentes aproximaciones y métodos en inferencia estadística, aplicados al problema de entrenamiento o ajuste de parámetros en Modelos Ocultos de Markov. Se tratarán los algoritmos EM (Expectation Maximization) y GEM (Generalized Expectation Maximization), el marco de modelos gráficos y sus algoritmos ML (Maximum Likelihood) y MAP (Maximum a Posteriori), así como modelos de conjunto, variacionales y métodos de muestreo MCMC (Markov Chain Montecarlo).

Texto completo:



Baldi, P., Chauvin, Y.: Smooth On-Line Learning Algorithms for Hidden Markov Models. Neural Cornputation 6, 307-318. (1994)

Baldi, P., Brunak, S.: Bioinformatics: the machine learning approach. Boston: MIT Press. (2001)

Baum, L. E., Petrie, Soules, G., Weiss, N.: “A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains” Ann. Math. Stat., vol. 41, no. 1, 164-171. (1970)

Beal, M. J., Ghahramani, Z., and Rasmussen, C. E.: The infinite hidden Markov model. Advances in Neural Information Processing Systems, volume 14. Cambridge: MIT Press. (2002)

Bengio, Y., Frasconi P.: Input/Output HMMs for sequence processing. IEEE Transactions on Neural Networks 7(5), 1231-1249. (1996)

Bilmes, J. A.: A gentle tutorial on the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden markov models. Technical Report ICSI-TR-97-02, University of Berkeley. (1998)

Bishop, C. M.: Pattern Recognition and Machine Learning. New York: Springer. (2006)

Blanchet, J., Vignes, M.: A Model-Based Approach to Gene Clustering with Missing Observation Reconstruction in a Markov Random Field Framework. En Journal of Computational Biology, Vol 16, No 3. 475-486. (2009)

Boufounos, P., El-Difrawy, S., Ehrlich, D.: Hidden Markov Models for DNA Sequencing. Proceedings of Workshop on Genomic Signal Processing and Statistics (GENSIPS 2002), Raleigh, NC, USA. (2002)

Cappé, O., Moulines, E. and Rydén, T.: Inference in Hidden Markov Models. New York: Springer. (2005)

Chu, W., Ghahramani, Z., Wild, D.: A graphical model for protein secondary structure prediction. En Proc. 21st Ann. Intl. Conf. on Machine Learning (ICML), Banff, Canada. (2004)

Davis, R., Lovell, B. C.: Comparing and evaluating hmm ensemble training algorithms using train and test and condition number criteria. Pattern Anal Appl 6(4). 327-335. (2003)

Dempster, A. P, Laird, N. M., Rubin, D. B.: Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society. Series B (Methodological), Vol. 39, No. 1., 1-38. (1977)

Elliott, R. J., Aggoun, L., Moore, J. B.: Hidden Markov Models Estimation and Control., 3ed. New York: Springer. (2008)

Ephraim, Y., Neri Merhav, N.: Hidden Markov Processes. IEEE Transactions on Information Theory, Vol. 48, No. 6. (2006).

Ghahramani, Z.: Graphical models: parameter learning. En Arbib, M. A. (Ed). The Handbook of Brain Theory and Neural Networks. Cambridge, MA: MIT Press. (1995)

Ghahramani, Z., M. Beal.: Graphical Models and Variational Methods. En M. Opper and D. Saad (Ed). Advanced Mean Field Methods - Theory and Practice. Cambridge, MA: MIT Press. (2001)

Heo, G., Woo, Y. W., Kim, K. B.: Properties of Ensemble Learning for Discrete Hidden Markov Models and Updating Prior Strategy. (2007)

Jaakkola, T. S.: Tutorial on variational approximation methods. En Advanced mean field methods. Cambridge, MA: MIT Press. (2001)

Jalen, L.: Some contributions to filtering theory with applications in financial modelling. Tesis Doctoral, Brunel University. (2009)

Jianfeng, G., Johnson, M.: A comparison of Bayesian estimators for unsupervised Hidden Markov Model POS taggers. En Proceedings of the 2008 Conference on Empirical Methods in Natural Language Processing. 344-352. (2008)

Jiao, F.: Probabilistic Graphical Models and Algorithms for Protein Problems. Tesis Doctoral, University of Waterloo. (2007)

Jordan, M., Ghahramani, Z., Jaakkola, T. S., Saul, L.: An introduction to variational methods for graphical models. En Learning in graphical models. 105-161. Cambridge, MA: MIT Press. (1999)

Jordan, M. I.: (Ed). Learning in Graphical Models. Cambridge, MA: MIT Press. (1999)

Jordan, M. I.: Graphical models, exponential families, and variational inference. UC Berkeley Dept. of Statistics, Tech. Rep. 629. (2003)

Jordan, M. I.: Graphical Models. Statist. Sci., 19, 140-155. (2004)

Ko, A. H. R., Sabourin, R., Britto A. Jr.: Ensemble of HMM classifiers based on the Clustering Validity Index for a Handwritten Numeral Recognizer. Pattern Analysis and Applications Journal. (2008)

Lauritzen, S. L.: Graphical Models. Oxford Science Publications. (1996)

Lawrence, N. D.: Variational inference guide. Technical report, The University Of Sheffield Machine Learning Group. (2002)

Lesk, A. M.: Introduction to Bioinformatics. New York: Oxford University Press Inc. (2002)

Liang, K., Wang, X., Anastassiou, D.: Bayesian Basecalling for DNA Sequence Analysis Using Hidden Markov Models. En IEEE/ACM Transactions on Compu- tational Biology and Bioinformatics 4, No. 3, 430-440. (2007)

Liang, K., Nettleton, D.: A Hidden Markov Model Approach to Testing Multiple Hypotheses on a Gene Ontology Graph. Dep. of Stat. Iowa State University. (2009)

Littlestone, N.: Learning quickly when irrelevant attributes abound: A new linearthreshold algorithm. Mach. Learning 2, 2, 285-318. (1988)

Littlestone, N., Warmuth, M. K.: The Weighted Majority algorithm. Information and Computation, 108, 212-261. (1994)

McGrory C. A., Titterington, D. M.: Variational Bayesian Analysis for Hidden Markov Models. En Australian & New Zealand J. of Stat. Vol, No 2, 227 - 244. (2009)

McKay, D. J. C.: Ensemble learning for hidden Markov models. Technical report, Cavendish Laboratory, University of Cambridge. (1997)

McKay, D. J. C.: Information Theory, Inference and Learning Algorithms. New York: Springer (2000)

McLachlan, G., Krishnan, T.: The EM Algorithm and Extension. New York: John Wiley and Sons. (1997)

Rabiner, L. R.: A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE 77(2), 257-286. (1989)

Rabiner, L., Juang, B. H.: Fundamentals of Speech Recognition. Prentice Hall Signal Processing Series. New Jersey: Prentice Hall. (1993)

Seligmann, C.: Uso de Modelos Escondidos de Markov en Biología Molecular Computacional., Poliantea No 9, Bogotá: Politécnico Grancolombiano. (2009)

Shinozaki, T., Furui, S.: Hidden mode HMM using bayesian network for modeling speaking rate fluctuation. Proc. of ASRU, (US Virgin Islands), 417-422. (2003)

Smyth, P., Heckerman, D., Jordan, M. I.: Probabilistic independence networks for hidden Markov probability models. Neural Computation, 9(2), 227-269. (1997)

Song, J., Liu, C., Song, Y., Qu, J., Hura, G. S.: Alignment of multiple proteins with an ensemble of Hidden Markov Models. International Journal of Data Mining and Bioinformatics. Vol 4, No 1, 60-71. (2010)

Stroock, D. W.: An Introduction to Markov Processes, Berlin: Springer. (2005)

Tusnády, G. E., Simon, I.: Principles Governing Amino Acid Composition of Integral Membrane Proteins: Application to Topology Prediction. J. Mol. Biol. No 283, 489-506. (1998)

Viterbi, A. J.: Error bounds for convolutional codes and an asymptotically optimal decoding algorithm. IEEE Transactions on Information Theory, Vol. 13, 260-269. (1967)

Werner M. J., Ide, K., Sornette, D.: Earthquake Forecasting Based on Data Assimi- lation: Sequential Monte Carlo Methods for Renewal Processes. (2009)

Wu, C. EJ.: On the convergence properties of the EM algorithm. Annals of Statistics, 11, 95-103. (1983).

Zhang, J., Ghahramani, Z., Yang, Y.: Learning Multiple Related Tasks using Latent Independent Component Analysis. Proceedings of NIPS 2005, Vancouver, Canada. (2005)

DOI: http://dx.doi.org/10.15765/e.v1i1.191

Enlaces refback

  • No hay ningún enlace refback.