project (one or two students
|Before 29/11||Send an email to instructors detailing the choice of project.|
|Before 04/12||Send a draft (1 page) + first results.|
your exam (secretariat or
|18/12||Poster session in Batiment
Cournot (C102-103) - 9am to 12pm
|Before 10/01||Submit your project report (~6 pages)|
|Probabilistics PCA||Interpretation of PCA as a graphical model
close to factorial analysis. A situation where EM has no local
Tipping, M. E., Bishop, C. M. 1999. Probabilistic principal component analysis. Journal of the Royal Statistical Society, Series B 61(3):611-622. [pdf]
|Learning graph structure - multinomial
||For complete discrete data, learning of
parameters and directed acyclic graph.
D. Heckerman, D. Geiger, D. Chickering. Learning Bayesian networks: The Combination of Knowledge and Statistical Data. Machine Learning, 20:197-243, 1995.
|Learning graph structure - Gaussian models
||For complete Gaussian data, learning of
parameters and directed acyclic graph.
D. Geiger, D. Heckerman. Learning Gaussian networks. Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, pp. 235--243.
|Variational methods for inference||Class of method for approximate inference.
An introduction to variational methods for graphical models. M. I. Jordan, Z. Ghahramani, T. S. Jaakkola, and L. K. Saul. In M. I. Jordan (Ed.), Learning in Graphical Models, Cambridge: MIT Press, 1999
Its application to Bayesian inference.
Beal, M.J. and Ghahramani, Z.
Variational Bayesian Learning of Directed Graphical Models with Hidden Variables
To appear in Bayesian Analysis 1(4), 2006.
|Simulation methods for inference (particle
||A simulation for dynamic graphical models
Chapter of "polycopie"
S. Arulampalam, S. Maskell, N. J. Gordon, and T. Clapp, A Tutorial on Particle Filters for On-line Non-linear/Non-Gaussian Bayesian Tracking, IEEE Transactions of Signal Processing, Vol. 50(2), pages 174-188, February 2002.
Doucet A., Godsill S.J. and Andrieu C., "On sequential Monte Carlo sampling methods for Bayesian filtering," Statist. Comput., 10, 197-208, 2000
|Semi-Markovian models||A class of models allowing to model the time
spent in any given state for a Markov Chain and an HMM.
Note from Kevin Murphy [pdf]
|Learning parameters in an undirected graphical model (Markov random fields)||Chapitet 9 of "polycopie" and articles.|
|Dynamic graphical models||Chapter of "polycopie". Specific topics to be defined.|
|General applications of the sum-product algorithms (e.g., to the FFT)||The
distributive law, S. M. Aji, R. J. Mceliece
Information Theory, IEEE Transactions on, Vol. 46, No. 2. (2000), pp. 325-343.
|Independent Component Analysis||A. Hyvärinen, E. Oja (2000): Independent
Component Analysis: Algorithms and Application, Neural
Networks, 13(4-5):411-430, 2000.
Course of Hervé LeBorgne: http://www.eeng.dcu.ie/~hlborgne/pub/th_chap3.pdf
Canonical Correlation Analysis
|CCA is analogous to PCA for the joint analysis of two random
vectors X and Y.
Clustering through a mixture of PCA
|M. E Tipping et C. M Bishop, “Mixtures of probabilistic principal component analyzers,” Neural computation 11, no. 2 (1999): 443–482.|
Stochastic relational models
Conditional Random Fields
|Charles Sutton, Andrew McCallum An Introduction to Conditional Random Fields for Relational Learning . In Lise Getoor and Ben Taskar, editors, Introduction to Statistical Relational Learning. MIT Press. 2007.|
|Z. Ghahramani et M. I Jordan, “Factorial
Markov models,” Machine
learning 29, no. 2 (1997): 245–273.
| M. Collins, S. Dasgupta, et R. E
generalization of principal component analysis to the exponential
family,” Advances in neural
information processing systems 1 (2002): 617–624.
Structure learning by L1 regularization
|J. Friedman, T. Hastie, et R.
covariance estimation with the graphical lasso,” Biostatistics
9, no. 3 (2008): 432.
Mixture of log-concave densities
| Interesting non-parametric
models for unimodal distributions.
distributions,” Computational Statistics & Data Analysis 51, no. 12
Constraint satisfaction and Sudoku
T. K Moon et J. H Gunther, “Multiple constraint satisfaction by
belief propagation: An example using sudoku,” dans Adaptive and
Learning Systems, 2006 IEEE Mountain Workshop on, 2006, 122–126.
of polycopie (ask login/pwd by e-mail)
A. Siepel et D. Haussler, “Phylogenetic hidden Markov models,” Statistical methods in molecular evolution (2005), 3, 325–351.
|Vision/Speech||Image segmentation by EM.
Blobworld: Image Segmentation Using Expectation-Maximization and Its Application to Image Querying; Chad Carson, Serge Belongie, Hayit Greenspan and Jitendra Malik. IEEE Trans. on Pattern Analysis and Machine Intelligence, 24(8), 1026-1038, August 2002.
Articles from Kevin Murphy:
"Using the Forest to See the Trees:A Graphical Model Relating Features, Objects and Scenes" Kevin Murphy, Antonio Torralba, William Freeman. NIPS'03 (Neural Info. Processing Systems)
Dynamic Bayesian Networks for Audio-Visual Speech Recognition A. Nefian, L. Liang, X. Pi, X. Liu and K. Murphy. EURASIP, Journal of Applied Signal Processing, 11:1-15, 2002
|Robotics||Automatic construction of maps)
Simultaneous Localization and Mapping with Sparse Extended Information Filters
Thrun et al. The International Journal of Robotics Research.2004;
(see also chapter of "polycopie" on Kalman filtering)
A. McCallum and K. Nigam. A comparison of event models for Naive Bayes text classification. In AAAI-98 Workshop on Learning for Text Categorization, 1998.
Latent Dirichlet allocation. D. Blei, A. Ng, and M. Jordan. Journal of Machine Learning Research, 3:993-1022, January 2003. [ .ps.gz | .pdf | code ]
|Text - Natural language processing||S. Vogel, H. Ney, and C. Tillmann.
HMM-based word alignment in statistical translation. In Proceedings
of the 16th conference on Computational linguistics, pp.
836-841, Morristown, NJ, USA, 1996. Association for Computational
Non contextual probabilistic grammars:
Notes de cours de CMU, 1999
|N most probable configurations||Implementation of an algorithm (HMM or more
complex graphs), from the following articles:
Dennis Nilsson, Jacob Goldberger. An Efficient Algorithm for Sequentially finding the N-Best List , IJCAI, 1999
Chen Yanover, Yair Weiss, Finding the M Most Probable Configurations Using Loopy Belief Propagation, NIPS 2003.
|Computation of tree-width||Comparing the classical heuristics and finer
Mark Hopkins and Adnan Darwiche
A Practical Relaxation of Constant-Factor Treewidth Approximation Algorithms
Proceedings of the First European Workshop on Probabilistic Graphical Models 2002
Also some exact methods
Stefan Arnborg, Derek G. Corneil, Andrzej Proskurowski, Complexity of finding embeddings in a k-tree, SIAM Journal on Algebraic and Discrete Methods (1997)