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 standard class projects need to contain the following 3 components:
The project should be done in groups of three students (to the extend possible). Groups of four are also exceptionally acceptable, but then we expect a more involved project justifying the number of people. For students who are asking for recommendation letters, please ask us about specific project requirements. Once you have an idea of a project, it is mandatory to have it validated by the teachers (by email, see instructions below) because we would like the projects undertaken to be as diverse as possible.
Note: 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. Note that joint projects have to be more ambitious and have to meet the expectations of both courses. So they are recommended only if you are very motivated.
November  Choose a project (one or two students per projects, preferably two) 
Before 11/18  Send an email to the three teachers, in which all members of your team are cc'ed to request our agreement on your choice of team and project topic. 
Before 12/09  Send a draft (1 page) + first results, on the Moodle. 
On 2017/01/04  Poster session in Batiment Cournot (C102103)  9am to 12pm 
Before 2017/01/11  Submit your project report (~6 pages, on the Moodle) 
Probabilistic PCA and Probabilistic CCA 
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):611622. [pdf] CCA (Canonical Correlation Analysis) is analogous to PCA for the joint analysis of two random vectors X and Y.

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, 20:197243, 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. 235243. 
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 Online Nonlinear/NonGaussian Bayesian Tracking, IEEE Transactions of Signal Processing, Vol. 50(2), pages 174188, February 2002. Doucet A., Godsill S.J. and Andrieu C., "On sequential Monte Carlo sampling methods for Bayesian filtering," Statist. Comput., 10, 197208, 2000 
SemiMarkovian 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)  Chapter 9 of "polycopie" and articles. 
Dynamic graphical models 
Chapter of "polycopie". Specific topics to be defined. 
General applications of the sumproduct 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. 325343. 
Independent Component Analysis  A. Hyvarinen, E. Oja (2000): Independent Component Analysis:
Algorithms and Application, Neural Networks, 13(45):411430,
2000. Course of Herve LeBorgne: http://www.eeng.dcu.ie/~hlborgne/pub/th_chap3.pdf

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): 443482. 
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. 
Dirichlet Process 

Factorial HMM 
Z. Ghahramani et M. I
Jordan, Factorial
hidden Markov models, Machine
learning 29, no. 2 (1997): 245273 
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): 617624. 
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 logconcave densities 
Interesting nonparametric
models for unimodal distributions. distributions, Computational Statistics & Data Analysis 51, no. 12 (2007): 62426251. 
Learning nonlinear dynamical systems 
Idea: use nonlinear
Kalman filters to learn the dynamics of a nonlinear dynamical system
form noisy observation of the system: Roweis, Sam, and Zoubin Ghahramani. Learning Nonlinear Dynamical Systems Using the Expectation–maximization Algorithm. Kalman Filtering and Neural Networks 6 (2001): 175–220. 
Hawkes process estimation 
Hawkes processes are
stochastic processes that allow to describe cascade or networks of
events that trigger one another via delayed selfexitation. It is
possible to design an EM algorithm to learn the structure of the
stochastic process Lewis, E., & Mohler, G. (2011). A nonparametric EM algorithm for multiscale Hawkes processes. Preprint. 
Particle Filtering 
Christian A. Naesseth, Fredrik
Lindsten, Thomas B. Schön (2014), Sequential Monte Carlo for Graphical Models See also the section on particle filter in chapter 21 of the polycopié 
Bioinformatics  Chapter
of polycopie (ask login/pwd by email) Phylogenetic HMM: A. Siepel et D. Haussler, Phylogenetic hidden Markov models, Statistical methods in molecular evolution (2005), 3, 325351. 
Vision/Speech  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 AudioVisual Speech Recognition A. Nefian, L. Liang, X. Pi, X. Liu and K. Murphy. EURASIP, Journal of Applied Signal Processing, 11:115, 2002 Optimization for MAP inference in computer vision: MRF Optimization via Dual Decomposition: MessagePassing Revisited, Komodakis, Paragios, Tziritas, ICVV 2007. Longer technical report version Learning tree structured context model for object recognition: In object recognition applying independent singleobject detectors may produce semantically incorrect results and even perfect detectors cannot solve contextrelated tasks in scene understanding. With a probabilistic graphical model it is possible to capture contextual information of a scene and apply it to object recognition and scene understanding problems. Choi, M. J., Torralba, A., & Willsky, A. S. (2012). A treebased context model for object recognition. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 34(2), 240252. 
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) 
Text  Naive Bayes: A. McCallum and K. Nigam. A comparison of event models for Naive Bayes text classification. In AAAI98 Workshop on Learning for Text Categorization, 1998. Latent Dirichlet allocation. D. Blei, A. Ng, and M. Jordan. Journal of Machine Learning Research, 3:9931022, January 2003. [ .ps.gz  .pdf  code ] 
Text  Natural language processing  S. Vogel, H. Ney, and C. Tillmann. HMMbased word
alignment in statistical translation. In Proceedings of the
16th conference on Computational linguistics, pp. 836841,
Morristown, NJ, USA, 1996. Association for Computational Linguistics. Non contextual probabilistic grammars: Notes de cours de CMU, 1999 
Connectionnist Temporal Classification 
An algorithm for recurrent neural network for classification along a sequence: Graves, A., Fernández, S., Gomez, F., & Schmidhuber, J. (2006). Connectionist temporal classification: labelling unsegmented sequence data with recurrent neural networks. In Proceedings of the 23rd International Conference on Machine Learning (pp. 369376). ACM. 
Restricted Boltzman Machines 
A probabilistic form of neural network: Fischer, A., & Igel, C. (2014). Training restricted Boltzmann machines: an introduction. Pattern Recognition, 47(1), 2539. 
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 NBest List , IJCAI, 1999 Chen Yanover, Yair Weiss, Finding the M Most Probable Configurations Using Loopy Belief Propagation, NIPS 2003. 
Computation of treewidth  Comparing the classical heuristics and
finer methods: Mark Hopkins and Adnan Darwiche A Practical Relaxation of ConstantFactor 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 ktree, SIAM Journal on Algebraic and Discrete Methods (1997) 