Learning latent tree graphical models

Journal of Machine Learning Research

Volumn 12, Issue , 2011, Pages 1771-1812

  Choi, Myung Jin ^a   Tan, Vincent Y F ^b   Anandkumar, Animashree ^c   Willsky, Alan S ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b University of Wisconsin Madison   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Graphical models; Hidden variables; Latent tree models; Markov random fields; Structure learning

Indexed keywords

GRAPHICAL MODEL; HIDDEN VARIABLE; MARKOV RANDOM FIELDS; STRUCTURE LEARNING; TREE MODELS;

APPROXIMATION ALGORITHMS; GRAPHIC METHODS; HIDDEN MARKOV MODELS; IMAGE SEGMENTATION; NUMERICAL METHODS; PLANT EXTRACTS; RANDOM VARIABLES; SPEECH RECOGNITION; VIRTUAL REALITY;

TREES (MATHEMATICS);

EID: 79960117913     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (52)

1. K. Atteson. The performance of neighbor-joining methods of phylogenetic reconstruction. Algorithmica, 25(2):251-278, 1999. (Pubitemid 129674400)
2. M. F. Balcan and P. Gupta. Robust hierarchical clustering. In Intl. Conf. on Learning Theory (COLT), 2010.
3. H.-J. Bandelth and A. Dress. Reconstructing the shape of a tree from observed dissimilarity data. Adv. Appl. Math, 7:309-43, 1986.
4. S. Bhamidi, R. Rajagopal, and S. Roch. Network delay inference from additive metrics. To appear in Random Structures and Algorithms, Arxiv preprint math/0604367, 2009.
5. R. Castro, M. Coates, G. Liang, R. Nowak, and B. Yu. Network tomography: Recent developments. Stat. Science, 19:499-517, 2004. (Pubitemid 40465976)
6. J. T. Chang and J. A. Hartigan. Reconstruction of evolutionary trees from pairwise distributions on current species. In Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, pages 254-257, 1991.
7. T. Chen, N. L. Zhang, and Y. Wang. Efficient model evaluation in the search based approach to latent structure discovery. In 4th European Workshop on Probabilistic Graphical Models, 2008.
8. M. J. Choi, J. J. Lim, A. Torralba, and A. S. Willsky. Exploiting hierarchical context on a large database of object categories. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), San Francisco, CA, June 2010.
9. C. K. Chow and C. N. Liu. Approximating discrete probability distributions with dependence trees. IEEE Trans. on Information Theory, 3:462-467, 1968.
10. T. Cormen, C. Leiserson, R. Rivest, and C. Stein. Introduction to Algorithms. McGraw-Hill Science/ Engineering/Math, 2nd edition, 2003.
11. T. M. Cover and J. A. Thomas. Elements of Information Theory. Wiley-Interscience, 2nd edition, 2006.
12. R. G. Cowell, A. P. Dawid, S. L. Lauritzen, and D. J. Spiegelhalter. Probabilistic Networks and Expert Systems. Statistics for Engineering and Information Science. Springer-Verlag, New York, 1999.
13. M. Csurös. Reconstructing Phylogenies in Markov Models of Sequence Evolution. PhD thesis, Yale University, 2000.
14. C. Daskalakis, E. Mossel, and S. Roch. Optimal phylogenetic reconstruction. In STOC '06: Proceedings of the Thirty-eighth Annual ACM Symposium on Theory of Computing, pages 159-168, 2006. (Pubitemid 44306549)
15. 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, 39:1-38, 1977.
16. R. Durbin, S. R. Eddy, A. Krogh, and G. Mitchison. Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. Cambridge Univ. Press, 1999.
17. G. Elidan and N. Friedman. Learning hidden variable networks: The information bottleneck approach. Journal of Machine Learning Research, 6:81-127, 2005.
18. P. L. Erdos, L. A. Székely, M. A. Steel, and T. J. Warnow. A few logs suffice to build (almost) all trees: Part ii. Theoretical Computer Science, 221:153-184, 1999.
19. J. Farris. Estimating phylogenetic trees from distance matrices. Amer. Natur., 106(951):645-67, 1972.
20. S. Harmeling and C. K. I. Williams. Greedy learning of binary latent trees. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010.
21. W. Hoeffding. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association, 58:13-30, 1958.
22. D. Hsu, S.M. Kakade, and T. Zhang. A spectral algorithm for learning hidden Markov models. In Intl. Conf. on Learning Theory (COLT), 2009.
23. A. K. Jain, M. N. Murthy, and P. J. Flynn. Data clustering: A review. ACM Computing Reviews, 1999.
24. T. Jiang, P. E. Kearney, and M. Li. A polynomial-time approximation scheme for inferring evolutionary trees from quartet topologies and its application. SIAM J. Comput., 30(6):194261, 2001.
25. C. Kemp and J. B. Tenenbaum. The discovery of structural form. Proceedings of the National Academy of Science, 105(31):10687-10692, 2008.
26. J. B. Kruskal. On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical Society, 7(1), Feb 1956.
27. M. R. Lacey and J. T. Chang. A signal-to-noise analysis of phylogeny estimation by neighborjoining: Insufficiency of polynomial length sequences. Mathematical Biosciences, 199:188-215, 2006. (Pubitemid 43197780)
28. J. A. Lake. Reconstructing evolutionary trees from dna and protein sequences: Parallnear distances. Proceedings of the National Academy of Science, 91:1455-1459, 1994.
29. S. L. Lauritzen. Graphical Models. Clarendon Press, 1996.
30. P. F. Lazarsfeld and N.W. Henry. Latent Structure Analysis. Boston: Houghton Mifflin, 1968.
31. D. G. Luenberger. Introduction to Dynamic Systems: Theory, Models, and Applications. Wiley, 1979.
32. D. Parikh and T. H. Chen. Hierarchical Semantics of Objects (hSOs). In ICCV, pages 1-8, 2007.
33. J. Pearl. Probabilistic Reasoning in Intelligent Systems: Network of Plausible inference. Morgan Kaufmann, 1988.
34. R. C. Prim. Shortest connection networks and some generalizations. Bell System Technical Journal, 36, 1957.
35. D. F. Robinson and L. R. Foulds. Comparison of phylogenetic trees. Mathematical Biosciences, 53: 131-147, 1981. (Pubitemid 11129084)
36. S. Roch. A short proof that phylogenetic tree reconstruction by maximum likelihood is hard. IEEE/ACM Trans. Comput. Biol. Bioinformatics, 3(1), 2006.
37. P. J. Rousseeuw. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Computational and Applied Mathematics, 20:53-65, 1987.
38. N. Saitou and M. Nei. The neighbor-joining method: a new method for reconstructing phylogenetic trees. Mol Biol Evol, 4(4):406-425, Jul 1987.
39. S. Sattath and A. Tversky. Additive similarity trees. Psychometrika, 42:319-45, 1977.
40. G. Schwarz. Estimating the dimension of a model. Annals of Statistics, 6:461-464, 1978.
41. R. J. Serfling. Approximation Theorems of Mathematical Statistics. Wiley-Interscience, Nov 1980.
42. S. Shen. Large deviation for the empirical correlation coefficient of two Gaussian random variables. Acta Mathematica Scientia, 27(4):821-828, Oct 2007.
43. R. Silva, R. Scheine, C. Glymour, and P. Spirtes. Learning the structure of linear latent variable models. Journal of Machine Learning Research, 7:191-246, Feb 2006. (Pubitemid 43668126)
44. L. Song, B. Boots, S. M. Siddiqi, G. Gordon, and A. Smola. Hilbert space embeddings of hidden Markov models. In Proc. of Intl. Conf. on Machine Learning, 2010.
45. K. St. John, T. Warnow, B.M.E. Moret, and L. Vawter. Performance study of phylogenetic methods: (unweighted) quartet methods and neighbor-joining. J. Algorithms, 48(1):173-193, 2003.
46. M. Steel. The complexity of reconstructing trees from qualitative characters and subtrees. Journal of Classification, 9:91-116, 1992.
47. V. Y. F. Tan, A. Anandkumar, and A. S. Willsky. Learning Gaussian tree models: Analysis of error exponents and extremal structures. IEEE Transactions on Signal Processing, 58(5):2701-2714, May 2010.
48. V. Y. F. Tan, A. Anandkumar, and A. S. Willsky. Learning high-dimensional Markov forest distributions: Analysis of error rates. Journal of Machine Learning Research (In Press), 2011.
49. Y. Tsang,M. Coates, and R. D. Nowak. Network delay tomography. IEEE Trans. Signal Processing, 51:21252136, 2003.
50. Y. Wang, N. L. Zhang, and T. Chen. Latent tree models and approximate inference in Bayesian networks. Journal of Artificial Intelligence Research, 32:879-900, Aug 2008.
51. N. L. Zhang. Hierarchical latent class models for cluster analysis. Journal of Machine Learning Research, 5:697-723, 2004.
52. N. L. Zhang and T Kǒcka. Efficient learning of hierarchical latent class models. In ICTAI, 2004. 181.