Discovering nonbinary hierarchical structures with Bayesian rose trees

Mixtures: Estimation and Applications

Volumn , Issue , 2011, Pages 161-187

  Blundell, Charles ^a   Teh, Yee Whye ^a   Heller, Katherine A ^b  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Avoiding needless cascades; Bayesian hierarchical clustering and Bayesian rose trees on same synthetic dataset; Bayesian rose tree mixture models; Dataset of three clusters of data items and no further internal substructure; Discovering nonbinary hierarchical structures with Bayesian rose trees; Greedy construction of Bayesian rose tree mixtures and Bayesian rose tree approach based on model selection; Important area for hierarchical structure discovery phylogenetic tree relating multiple species; Prior work, diverse range of methods for hierarchical structure discovery; Rich hierarchical structures common across disciplines; Rose trees, partitions and mixtures

Indexed keywords

MIXTURES;

BAYESIAN; DATA ITEMS; HIERARCHICAL STRUCTURES; PHYLOGENETIC TREES; ROSE TREE;

TREES (MATHEMATICS);

EID: 84864706570     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781119995678.ch8     Document Type: Chapter

References (45)

1. Aldous, D., Krikun, M. and Popovic, L. (2008) Stochastic models for phylogenetic trees on higher-order taxa. Journal of Mathematical Biology, 56, 525-557.
2. Barry, D. and Hartigan, J. A. (1992) Product partition models for change point problems. Annals of Statistics, 20, 260-279.
3. Bertoin, J. (2001) Homogeneous fragmentation processes. Probability Theory and Related Fields, 121, 301-318.
4. Bird, R. (1998) Introduction to Functional Programming using Haskell, 2nd edn. Prentice Hall.
5. Blei, D. M., Griffiths, T. L. and Jordan, M. I. (2010) The nested Chinese restaurant process and Bayesian nonparametric inference of topic hierarchies. Journal of the Association for Computing Machines, 57, 1-30.
6. Camin, J. H. and Sokal, R. R. (1965) A method for deducing branching sequences in phylogeny. Evolution, 19, 311-326.
7. Cree, G. S. and McRae, K. (2003) Analyzing the factors underlying the structure and computation of the meaning of chipmunk, cherry, chisel, cheese and cello (and many other such concrete nouns). Journal of Experimental Psychology: General, 132, 163-201.
8. Duda, R. O. and Hart, P. E. (1973) Pattern Classification and Scene Analysis. JohnWiley & Sons, Inc., New York.
9. Felsenstein, J. (1973) Maximum likelihood estimation of evolutionary trees from continuous characters. American Journal of Human Genetics, 25, 471-492.
10. Felsenstein, J. (1981) Evolutionary trees from DNA sequences: a maximum likelihood approach. Journal of Molecular Evolution, 17, 368-376.
11. Felsenstein, J. (2003) Inferring Phylogenies. Sinauer Associates.
12. Fitch, W. M. and Margoliash, E. (1967) Construction of phylogenetic trees. Science, 155, 279-284.
13. Frank, A. and Asuncion, A. (2010) UCI machine learning repository.
14. Friedman, N. (2003) Pcluster: Probabilistic agglomerative clustering of gene expression profiles. Technical Report 2003-80, Hebrew University.
15. Girvan, M. and Newman, M. E. J. (2002) Community structure in social and biological networks. In Proceedings of the National Academy of Sciences of the USA, Vol. 99, pp. 7821-7826.
16. Hartigan, J. A. (1972) Direct clustering of a data matrix. Journal of the American Statistical Association, 67, 123-129.
17. Hartigan, J. A. (1975) Clustering Algorithms. John Wiley & Sons, Ltd.
18. Heller, K. A. (2008) Efficient Bayesian methods for clustering. PhD thesis, Gatsby Computational Neuroscience Unit, University College London.
19. Heller, K. A. and Ghahramani, Z. (2005) Bayesian hierarchical clustering. In International Conference on Machine Learning, Vol. 22.
20. Huelsenbeck, J. P. and Ronquist, F. (2001) MRBAYES: Bayesian inference of phylogenetic trees. Bioinformatics, 17, 754-755.
21. Jain, A. K., Murty, M. N. and Flynn, P. J. (1999) Data clustering: a review. ACM Computer Surveys, 31, 264-323.
22. Kaufman, L. and Rousseeuw, P. J. (1990) Finding Groups in Data. JohnWiley & Sons, Ltd.
23. Kemp, C. C., Griffiths, T. L., Stromsten, S. and Tenenbaum, J. B. (2004) Semi-supervised learning with trees. In Advances in Neural Information Processing Systems, Vol. 16 (eds S. Thrun, L. Saul and B. Schölkop). MIT Press.
24. McCallum, A. K. (1996) Bow: a toolkit for statistical language modelling, text retrieval, classification and clustering. http://www.cs.cmu.edu/ mccallum/bow.
25. McLachlan, G. J. and Basford, K. E. (1988) Mixture Models: Inference and Applications to Clustering. Marcel Dekker.
26. Meeds, E. and Osindero, S. (2006) An alternative infinite mixture of Gaussian process experts. In Advances in Neural Information Processing Systems, Vol. 18 (eds Y. Weiss, B. Schölkop and J. Platt), pp. 883-890. MIT Press.
27. Meertens, L. (1988) First steps towards the theory of rose trees.Working Paper 592 ROM-25, IFIP Working Group 2.1.
28. Müller, P. and Quintana, F. A. (2010) Random partition models with regression on covariates. Journal of Statistical Inference and Planning, 140, 2801-2808.
29. Murtagh, F. (1983) A survey of recent advances in hierarchical clustering algorithms. Computer Journal, 26, 254-259.
30. Neal, R. M. (2003) Density modelling and clustering using Dirichlet diffusion trees. In Bayesian Statistics 7 (eds J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West), pp. 619-629. Oxford University Press.
31. Pitman, J. (1999) Coalescents with multiple collisions. Annals of Probability, 27, 1870-1902.
32. Rasmussen, C. E. and Ghahramani, Z. (2002) Infinite mixtures of Gaussian process experts. In Advances in Neural Information Processing Systems, Vol. 14 (eds T. G. Dietterich, S. Becker and Z. Ghahramani), pp. 881-888. MIT Press.
33. Rogers, J. S. (1997) On the consistency of maximum likelihood estimation of phylogenetic trees from nucleotide sequences. Systems Biology, 42, 354-357.
34. Rosch, E., Mervis, C., Gray, W., Johnson, D. and Boyes-Braem, P. (1976) Basic objects in natural categories. Cognitive Psychology, 8 382-439.
35. Roy, D. M., Kemp, C., Mansinghka, V. and Tenenbaum, J. B. (2007) Learning annotated hierarchies from relational data. In Advances in Neural Information Processing Systems, Vol. 19 (eds B. Cholkopf, J. Platt and T. Hoffman), pp. 1185-1192. MIT Press.
36. Saitou, N. and Nei, M. (1987) The neighbor-joining method: a newmethod for reconstructing phylogenetic trees. Molecular Biology and Evolution, 4, 406-425.
37. Segal, E., Koller, D. and Ormoneit, D. (2002) Probabilistic abstraction hierarchies. In Advances in Neural Information Processing Systems, Vol. 14 (eds T. G. Dietterich, S. Becker and Z. Ghahramani). MIT Press.
38. Studier, J. A. and Keppler, K. J. (1988) A note on the neighbor-joining algorithm of Saitou and Nei. Molecular Biology and Evolution, 14, 210-211.
39. Teh, Y. W., Daume III, H. and Roy, D. M. (2008) Bayesian agglomerative clustering with coalescents. In Advances in Neural Information Processing Systems, Vol. 20 (eds J. C. Platt, D. Koller, Y. Singer and S. Roweis), pp. 1473-1480. MIT Press.
40. Vaithyanathan, S. and Dom, B. (2000) Model-based hierarchical clustering. In Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence, pp. 599-608. UAI Press.
41. Williams, C. K. I. (2000)AMCMCapproach to hierarchical mixture modelling. In Advances in Neural Information Processing Systems, Vol. 12 (eds S. A. Solla, T. K. Leen and K.-R. Muller). MIT Press.
42. Williams, C. and Seeger,M. (2001) Using the Nyström method to speed up kernel methods. In Advances in Neural Information Processing, Vol. 13 (eds T. K. Leen, T. G. Diettrich, and V. Tresp). MIT Press.
43. Xu, Y., Heller, K. A. and Ghahramani, Z. (2009) Tree-based inference for Dirichlet process mixtures. In JMLR Workshop and Conference Proceedings Volume 5: AISTATS 2009, (eds D. van Dyk and M. Welling), pp. 623-630.
44. Yang, Z. (1994) Statistical properties of the maximum likelihood method of phylogenetic estimation and comparison with distance matrix methods. Systematic Biology, 43, 329-342.
45. Yang, Z. and Rannala, B. (1997) Bayesian phylogenetic inference using DNA sequences: a Markov chain Monte Carlo method. Molecular Biology and Evolution, 14, 717-724.