Introduction to probabilistic graphical models

Class projects


The project gives you the opportunity to study in greater depth certain concepts of the course. The topic has to be linked with algorithms, concepts or methods presented in class, but beyond this requirement, the choice is quite open. In particular, it may be tailored to your interests.

The class projects may have the following form:
    * An article review around a given topic (research articles or "polycopie" not studied in class). See below a list of tentative projects.
    * Application project: application of the methods seen in class to a given problem of interest (e.g., in computer vision, signal processing, artificial intelligence, control, etc.). The project may be done jointly with another class (with the formal agreement of the corresponding teachers). For joint projects between GM and Object recognition and computer vision course, get in touch with I. Laptev and J. Sivic.
    * Theoretical or methodological project.

The project may be done alone or in groups of two. Once you have an idea of a project, it is mandatory to have it validated by the teachers (by email). In particular, if possible, all students/groups of two students have to have a different project.


The final class project makes a third of the final grade for the class. Evaluation will be made on:
    * A report (less than 6 pages) presenting the project and the obtained results (for applicative projects), to be given by January 10th, 2014. The report has to be written in such a way that any student who has followed the class can understand (no need to introduce graphical model concepts). The report has to clearly present (in French or English) the studied problem and the existing approaches. You will be more evaluated on the clarity of the report rather than on its length.
    * A poster presentation of 5 minutes, from at most 8 A4 pages which will displayed on the wall (Wednesday December 18th, 2013, from 9am to 12pm in room C102-C103, Batiment Cournot, ENS Cachan). The presentation (in French or English) is also geared towards other students and the goal is to highlight in the allocated time the salient points. Like in a regular conference poster session, students are encouraged to attend other student posters.

(1) Each student or group of students has to obtained the agreement of teachers (by email) before November 29, 2013.
(2) Each student or group of students has to submit a small mid-project report (one page, as a latex or text document) presenting the progress and the obtained results, so that some feedback may be given. This report has to be sent by email before December 4th, 2013.


The various steps are summarized below.

Mid-november Choose a project (one or two students per projects)
Before 29/11 Send an email to instructors detailing the choice of project.
Before 04/12 Send a draft (1 page) + first results.
Before 18/12 Submit your exam (secretariat or email).
18/12 Poster session in Batiment Cournot (C102-103) - 9am to 12pm
Before 10/01 Submit your project report (~6 pages)

Article or chapter review

The goal of this list of projects is to show classical (and if possible interesting) articles using or improving graphical models. This may give you an idea of current research topics as well as applicative projects. Even if you don't select any of these, reading some of them is advised.

Probabilistics PCA Interpretation of PCA as a graphical model close to factorial analysis. A situation where EM has no local minima.

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 models
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 filtering)
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 generalized 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:
Jean-François Cardoso Dependence, Correlation and Gaussianity in Independent Component Analysis. Journal of Machine Learning Research 4(Dec):1177--1203, 2003. [pdf]

Canonical Correlation Analysis

CCA is analogous to PCA for the joint analysis of two random vectors X and Y.
  1. D. R Hardoon, S. Szedmak, et J. Shawe-Taylor, “Canonical correlation analysis: an overview with application to learning methods,” Neural Computation 16, no. 12 (2004): 2639–2664. 
  2. F. R Bach et M. I Jordan, “A probabilistic interpretation of canonical correlation analysis,” Dept. Statist., Univ. California, Berkeley, CA, Tech. Rep 688 (2005). 

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
  • E. M Airoldi et al., “Mixed membership stochastic block models for relational data with application to protein-protein interactions,” dans Proceedings of the International Biometrics Society Annual Meeting, 2006.

  • 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.

     Dirichlet Process
  • R. M Neal, “Markov chain sampling methods for Dirichlet process mixture models,” Journal of computational and graphical statistics 9, no. 2 (2000): 249–265. 
  • Y. W Teh, “Dirichlet Process,” Submitted to Encyclopedia of Machine Learning (2007). 
  • A. Ranganathan, “The Dirichlet Process Mixture (DPM) Model” (2004). 

  • Factorial HMM
    Z. Ghahramani et M. I Jordan, “Factorial hidden Markov models,” Machine learning 29, no. 2 (1997): 245–273. 

    Generalized PCA
    M. Collins, S. Dasgupta, et R. E Schapire, “A 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. Tibshirani, “Sparse inverse covariance estimation with the graphical lasso,” Biostatistics 9, no. 3 (2008): 432. 

    Mixture of log-concave densities

     Interesting non-parametric models for unimodal distributions.

  • T Chang et G. Walther, “Clustering with mixtures of log-concave
    ,” Computational Statistics & Data Analysis 51, no. 12
    (2007): 6242–6251.
  • G. Walther, “Inference and modeling with log-concave distributions,” Statistical Science 25 (2010).

  • 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.

    Examples of applications of Graphical modeles

    These articles present classical applications. They may give you ideas for an applicative project or may be used for article reviews.

    Bioinformatics Chapter of polycopie (ask login/pwd by e-mail)

    Phylogenetic HMM:
    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; 23: 693-716.
    (see also chapter of "polycopie" on Kalman filtering)
    Text Naive Bayes:
    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 Linguistics.

    Non contextual probabilistic grammars:
    Notes de cours de CMU, 1999

    Implementation of algorithms

    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 methods:

    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)