A spectral algorithm for learning Hidden Markov Models

Journal of Computer and System Sciences

Volumn 78, Issue 5, 2012, Pages 1460-1480

  Hsu, Daniel ^a   Kakade, Sham M ^b   Zhang, Tong ^a  

^a RUTGERS UNIVERSITY   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Hidden Markov Models; Latent variable models; Learning probability distributions; Observable operator models; Singular value decomposition; Spectral algorithm; Time series; Unsupervised learning

Indexed keywords

COMPUTATIONAL COMPLEXITY; HEURISTIC ALGORITHMS; HIDDEN MARKOV MODELS; LEARNING SYSTEMS; NATURAL LANGUAGE PROCESSING SYSTEMS; PROBABILITY DISTRIBUTIONS; SINGULAR VALUE DECOMPOSITION; STATISTICAL MECHANICS; TIME SERIES; UNSUPERVISED LEARNING;

CRYPTOGRAPHIC ASSUMPTIONS; HIDDEN MARKOV MODELS (HMMS); LATENT VARIABLE MODELS; LEARNING PROBABILITY DISTRIBUTIONS; MATRIX MULTIPLICATION; NATURAL LANGUAGE PROCESSING; OBSERVABLE OPERATOR MODELS; SPECTRAL ALGORITHM;

LEARNING ALGORITHMS;

EID: 84863414476     PISSN: 00220000     EISSN: 10902724     Source Type: Journal    
DOI: 10.1016/j.jcss.2011.12.025     Document Type: Conference Paper

References (33)

1. S. Andersson, T. Ryden, and R. Johansson Linear optimal prediction and innovations representations of hidden Markov models Stochastic Process. Appl. 108 2003 131 149
2. Leonard E. Baum, and J.A. Eagon An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology Bull. Amer. Math. Soc. 73 3 1967 360 363
3. Leonard E. Baum, Ted Petrie, George Soules, and Norman Weiss A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains Ann. of Math. Statist. 41 1 1970 164 171
4. S. Charles Brubaker, Santosh Vempala, Isotropic PCA and affine-invariant clustering, in: FOCS, 2008.
5. J.W. Carlyle, and A. Paz Realization by stochastic finite automaton J. Comput. System Sci. 5 1971 26 40
6. Kamalika Chaudhuri, Satish Rao, Learning mixtures of product distributions using correlations and independence, in: COLT, 2008.
7. T.M. Cover, and J.A. Thomas Elements of Information Theory 1991 Wiley
8. G. Cybenko, V. Crespi, Learning Hidden Markov Models using non-negative matrix factorization, Technical report, 2008, arXiv:0809.4086.
9. Sanjoy Dasgupta, Learning mixutres of Gaussians, in: FOCS, 1999.
10. Sanjoy Dasgupta, and Leonard Schulman A probabilistic analysis of EM for mixtures of separated, spherical Gaussians J. Mach. Learn. Res. 8 February 2007 203 226
11. A.P. Dempster, N.M. Laird, and D.B. Rubin Maximum likelihood from incomplete data via the EM algorithm J. R. Stat. Soc. Ser. B Stat. Methodol. 39 1 1977 1 38
12. Even-Dar Eyal, Sham M. Kakade, Yishay Mansour, Planning in POMDPs using multiplicity automata, in: UAI, 2005.
13. Even-Dar Eyal, Sham M. Kakade, Yishay Mansour, The value of observation for monitoring dynamic systems, in: IJCAI, 2007.
14. M. Fliess Matrices deHankel J. Math. Pures Appl. 53 1974 197 222
15. H. Hotelling The most predictable criterion J. Educ. Psychol. 1935
16. Herbert Jaeger Observable operator models for discrete stochastic time series Neural Comput. 12 6 2000
17. H. Jaeger, M. Zhao, K. Kretzschmar, T. Oberstein, D. Popovici, and A. Kolling Learning observable operator models via the es algorithm S. Haykin, J. Principe, T. Sejnowski, J. McWhirter, New Directions in Statistical Signal Processing: From Systems to Brain 2006 MIT Press 417 464
18. T. Katayama Subspace Methods for System Identification 2005 Springer
19. M. Kearns, Y. Mansour, D. Ron, R. Rubinfeld, R. Schapire, L. Sellie, On the learnability of discrete distributions, in: STOC, 1994, pp. 273-282.
20. Michael Littman, Richard Sutton, Singh Satinder, Predictive representations of state, in: Advances in Neural Information Processing Systems 14 (NIPS), 2001, pp. 1555-1561.
21. L. Ljung System Identification: Theory for the User 1987 Prentice Hall Englewood Cliffs, NJ
22. C. McDiarmid On the method of bounded differences Surveys in Combinatorics 1989 Cambridge University Press 148 188
23. E. Mossel, and S. Roch Learning nonsingular phylogenies and Hidden Markov Models Ann. Appl. Probab. 16 2 2006 583 614
24. P.V. Overschee, and B. De Moor Subspace Identification of Linear Systems 1996 Kluwer Academic Publishers
25. Lawrence R. Rabiner A tutorial on Hidden Markov Models and selected applications in speech recognition Proc. IEEE 77 2 1989 257 286
26. M.P. Schützenberger On the definition of a family of automata Inform. Control 4 1961 245 270
27. S.M. Siddiqi, B. Boots, G.J. Gordon, Reduced-rank Hidden Markov Models, in: Proceedings of the 13th International Conference on Artificial Intelligence and Statistics, 2010.
28. Le Song, Byron Boots, Sajid M. Siddiqi, Geoffrey J. Gordon, Alex Smola, Hilbert space embeddings of Hidden Markov Models, in: Proceedings of the 27th International Conference on Machine Learning, 2010.
29. G.W. Stewart, and Ji-Guang Sun Matrix Perturbation Theory 1990 Academic Press New York
30. Sebastiaan Terwijn, On the learnability of Hidden Markov Models, in: International Colloquium on Grammatical Inference, 2002.
31. B. Vanluyten, J. Willems, B. De Moor, A new approach for the identification of Hidden Markov Models, in: Conference on Decision and Control, 2007.
32. Santosh Vempala, Grant Wang, A spectral algorithm for learning mixtures of distributions, in: FOCS, 2002.
33. MingJie Zhao, Herbert Jaeger, The error controlling algorithm for learning OOMs, Technical report 6, International University Bremen, 2007.