Nevin L Zhang Dept of Computer Science amp Engineering The Hong Kong Univ of Sci amp Tech httpwwwcseusthklzhang AAAI 2014 Tutorial HKUST 2014 HKUST 1988 Latent Tree Models ID: 621896
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Latent Tree Models
Nevin L. ZhangDept. of Computer Science & EngineeringThe Hong Kong Univ. of Sci. & Tech.http://www.cse.ust.hk/~lzhang
AAAI 2014 TutorialSlide2
HKUST
2014
HKUST
1988Slide3
Latent Tree Models
Part I: Non-Technical Overview (25 minutes)Part II: Definition and Properties (25 minutes)Part III: Learning Algorithms (110 minutes, 30 minutes break half way)Part IV: Applications (50
minutes)Slide4
Part I: Non-Technical Overview
Latent tree modelsWhat can LTMs be used for:Discovery of co-occurrence/correlation patterns
Discovery of latent variable/structuresMultidimensional clusteringExamplesDanish beer survey dataText dataSlide5
Latent Tree Models (LTMs)
Tree-structured probabilistic graphical modelsLeaves observed (manifest variables)Discrete or continuousInternal nodes latent (latent variables)DiscreteEach edge is associated with a conditional distributionOne node with marginal distribution
Defines a joint distributions over all the variables(Zhang, JMLR 2004)Slide6
Latent Tree Analysis (LTA)
Learning latent tree models: Determine
Number of latent variables
Numbers of possible states for latent variables
Connections among nodes
Probability distributions
From data on observed variables, obtain latent tree modelSlide7
LTA on Danish Beer Market Survey Data
463 consumers, 11 beer brands Questionnaire: For each brand:Never seen the brand before (s0); Seen before, but never tasted (s1); Tasted, but do not drink regularly (s2) Drink regularly (s3).
Page
7
(
Mourad et al. JAIR 2013)Slide8
Why variables grouped as such?
Responses on brands in each group strongly correlated.GronTuborg and Carlsberg: Main mass-market beersTuborgClas and CarlSpec: Frequent beers, bit darker than the aboveCeresTop, CeresRoyal, Pokal, …: minor local beers
In general, LTA partitions observed variables into groups such thatVariables in each group are strongly correlated, andThe correlations among each group can be properly be modeled using one single latent variable
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8Slide9
Multidmensional Clustering
Each Latent variable gives a partition of consumers. H1: Class 1: Likely to have tasted TuborgClas, Carlspec and Heineken , but do not drink regularlyClass 2: Likely to have seen or tasted the beers, but did not drink regularly
Class 3: Likely to drink TuborgClas and Carlspec regularlyH0 and H2 give two other partitions.In general, LTA is a technique for
multiple clustering
.
In contrast, K-Means, mixture models give only one partition.Page 9Slide10
Unidimensional vs Multidimensional Clustering
Grouping of objects into clusters such that objects in the same cluster are similar while objects from different clusters are dissimilar.
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10
Result of clustering is often a partition of all the objects.Slide11
How to Cluster Those?Slide12
How to Cluster Those?
Style of pictureSlide13
How to Cluster Those?
Type of object in pictureSlide14
Multidimensional Clustering
Complex data usually have
multiple facets
and can
be meaningfully partitioned in multiple ways
. Multidimensional clustering /
Multi-Clustering
LTA is a model-based method for multidimensional clustering.
O
ther methods: http
://www.siam.org/meetings/sdm11/clustering.pdfSlide15
LTA produces a partition of observed variables.
For each cluster of variables, it produces a partition of objects.Clustering of Variables and ObjectsSlide16
1041 web pages collected from 4 CS departments in
1997 336 wordsBinary Text Data: WebKBSlide17
Latent Tree Model for WebKB
Data
(Liu et al. MLJ 2013)
89 latent variables Slide18
Latent Tree Modes for WebKB DataSlide19Slide20Slide21
Words in each group tend to co-occur.
On binary text data, LTA partitions word variables into groups such thatWords in each group tend to co-occur andThe correlations can be properly be explained using one single latent variableWhy variables grouped as such?
LTA is a method for identifying co-occurrence relationships.Slide22
LTA is
an alternative approach to topic detectionY66=4: Object Oriented Programming (oop)Y66=2: Non-oop programmingY66=1: programming languageY66=3: Not on programmingMultidimensional
Clustering
More on this in Part IVSlide23
Summary
Latent tree models:Tree-structured probabilistic graphical modelsLeaf nodes: observed variablesInternal nodes: latent variableWhat can LTA be used for:Discovery of co-occurrence patterns in binary dataDiscovery of correlation patterns in general discrete dataDiscovery of latent variable/structuresMultidimensional clusteringTopic detection in text dataProbabilistic modellingSlide24
Key References:
Anandkumar, A., Chaudhuri, K., Hsu, D., Kakade, S. M., Song, L., & Zhang, T. (2011). Spectral methods for learning multivariate latent tree structure. In Twenty-Fifth Conference in Neural Information Processing Systems (NIPS-11).Anandkumar, A., Ge, R., Hsu, D., Kakade, S.M., and Telgarsky, M. Tensor decompositions for learning latent variable models. In Preprint,
2012a.Anandkumar, A., Hsu, D., and Kakade, S. M. A method of moments for mixture models and hidden Markov models. In An abridged version appears in the Proc. Of COLT, 2012b.Choi, M. J., Tan, V. Y.,
Anandkumar
, A., &
Willsky, A. S. (2011). Learning latent tree graphical models. Journal of Machine Learning Research, 12, 1771–1812.Friedman, N., Ninio, M., Pe’er, I., & Pupko, T. (2002). A structural EM algorithm for phylogenetic inference.. Journal of Computational Biology, 9(2), 331–353.Harmeling, S., & Williams, C. K. I. (2011). Greedy learning of binary latent trees. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(6), 1087–1097.Hsu, D., Kakade, S., & Zhang, T. (2009). A spectral algorithm for learning hidden Markov models. In The 22nd Annual Conference on Learning Theory (COLT 2009).Slide25
Key References:
E. Mossel, S. Roch, and A. Sly. Robust estimation of latent tree graphical models: Inferring hidden states with inexact parameters. Submitted. http://arxiv.org/abs/1109.4668, 2011.Mourad, R., Sinoquet, C., & Leray, P. (2011). A hierarchical Bayesian network approach for linkage disequilibrium modeling and data-dimensionality reduction prior to genomewide
association studies. BMC Bioinformatics, 12, 16.Mourad R., Sinoquet C., Zhang N. L., Liu T. F. and Leray P. (2013). A survey on latent tree models and applications. Journal of Artificial Intelligence Research, 47, 157-203 , 13 May 2013. doi:10.1613/jair.3879.
Parikh, A. P., Song, L., & Xing, E. P. (2011). A spectral algorithm for latent tree
graphical models
. In Proceedings of the 28th International Conference on Machine Learning (ICML-2011).Saitou, N., & Nei, M. (1987). The neighbor-joining method: A new method for reconstructing phylogenetic trees.. Molecular Biology and Evolution, 4(4), 406–425.Song, L., Parikh, A., & Xing, E. (2011). Kernel embeddings of latent tree graphical models. In Twenty-Fifth Conference in Neural Information Processing Systems (NIPS-11).Tan, V. Y. F., Anandkumar, A., & Willsky, A. (2011). Learning high-dimensional Markov forest distributions: Analysis of error rates. Journal of Machine Learning Research,12, 1617–1653.Slide26
Key References:
T. Chen and N. L. Zhang (2006). Quartet-based learning of shallow latent variables. In Proceedings of the Third European Workshop on Probabilistic Graphical Model,59-66 , September 12-15, 2006.Chen, T., Zhang, N. L., Liu, T., Poon, K. M., & Wang, Y. (2012). Model-based multidimensional clustering of categorical data. Artificial Intelligence, 176(1), 2246–2269.Liu, T. F., Zhang, N. L., Liu, A. H., & Poon, L. K. M. (2013). Greedy learning of latent tree models for multidimensional clustering. Machine Learning, doi:10.1007/s10994-013-5393-0.Liu, T. F., Zhang, N. L., and Chen, P. X. (2014). Hierarchical latent tree analysis for topic detection. ECML, 2014 Poon, L. K. M., Zhang, N. L., Chen, T., & Wang, Y. (2010). Variable selection in
modelbased clustering: To do or to facilitate. In Proceedings of the 27th International Con-ference on Machine Learning (ICML-2010).Wang, Y., Zhang, N. L., & Chen, T. (2008). Latent tree models and approximate inference in Bayesian networks. Journal of Articial Intelligence Research, 32, 879–900.
Wang, X. F.,
Guo
, J. H., Hao, L. Z., Zhang, N.L., & P. X. Chen (2013). Recovering discrete latent tree models by spectral methods. Wang, X. F., Zhang, N. L. (2014). A Study of Recently Discovered Equalities about Latent Tree Models using Inverse Edges. PGM 2014.Zhang, N. L. (2004). Hierarchical latent class models for cluster analysis. The Journal of Machine Learning Research, 5, 697–723.Zhang, N. L., & Kocka, T. (2004a). Effective dimensions of hierarchical latent class models. Journal of Articial Intelligence Research, 21, 1–17.Slide27
Key References:
Zhang, N. L., & Kocka, T. (2004b). Efficient learning of hierarchical latent class models. In Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence (ICTAI), pp. 585–593.Zhang, N. L., Nielsen, T. D., & Jensen, F. V. (2004). Latent variable discovery in classification models. Artificial Intelligence in Medicine, 30(3), 283–299.Zhang, N. L., Wang, Y., & Chen, T. (2008). Discovery of latent structures: Experience with the CoIL Challenge 2000 data set*. Journal of Systems Science and
Complexity, 21(2), 172–183.Zhang, N. L., Yuan, S., Chen, T., & Wang, Y. (2008). Latent tree models and diagnosis in traditional Chinese medicine. Artificial Intelligence in Medicine, 42(3), 229–245.Zhang, N. L., Yuan, S., Chen, T., & Wang, Y. (2008). Statistical Validation of TCM Theories. Journal of Alternative and Complementary Medicine, 14(5):583-7.
Zhang, N. L., Fu, C., Liu, T. F., Poon, K. M., Chen, P. X., Chen, B. X., Zhang, Y. L.
(2014). The Latent Tree Analysis Approach to Patient
Subclassification in Traditional Chinese Medicine. Evidence-Based Complementary and Alternative Medicine.Xu, Z. X., Zhang, N. L., Wang, Y. Q., Liu, G. P., Xu, J., Liu, T. F., and Liu A. H. (2013). Statistical Validation of Traditional Chinese Medicine Syndrome Postulates in the Context of Patients with Cardiovascular Disease. The Journal of Alternative and Complementary Medicine. 18, 1-6.Zhao, Y. Zhang , N. L., Wang, T. F., Wang, Q. G. (2014). Discovering Symptom Co-Occurrence Patterns from 604 Cases of Depressive Patient Data using Latent Tree Models. The Journal of Alternative and Complementary Medicine. 20(4):265-71.