The reading 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 work expected for the paper reading is to read one or several research papers (this depends on the topic you choose) and to write a report that presents the method in detail. In particular, we expect that the main technical ideas of the method will be presented with the appropriate level of details and equations in the report. If libraries are available that already implement the method, simple experiments can complement the presentation of the method, but we are not expecting that you implement complicated algorithms.
The project should be done in groups of three students (to the extend possible). Once you have chosen the reading you would like to do, it is mandatory to have it validated by the teachers (by email, see instructions below) because we would like the readings undertaken to be as diverse as possible.
| 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):611-622. [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, 20:197-243, 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) | Chapter 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. Hyvarinen, E. Oja (2000): Independent Component Analysis:
Algorithms and Application, Neural Networks, 13(4-5):411-430,
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): 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. |
Dirichlet Process |
|
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. distributions, Computational Statistics & Data Analysis 51, no. 12 (2007): 6242-6251. |
Learning non-linear dynamical systems |
Idea: use non-linear
Kalman filters to learn the dynamics of a non-linear 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 self-exitation. 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 e-mail) Phylogenetic HMM: A. Siepel et D. Haussler, Phylogenetic hidden Markov models, Statistical methods in molecular evolution (2005), 3, 325-351. |
| 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 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 Optimization for MAP inference in computer vision: MRF Optimization via Dual Decomposition: Message-Passing Revisited, Komodakis, Paragios, Tziritas, ICVV 2007. Longer technical report version Learning tree structured context model for object recognition: In object recognition applying independent single-object detectors may produce semantically incorrect results and even perfect detectors cannot solve context-related 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 tree-based context model for object recognition. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 34(2), 240-252. |
| 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 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 |
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. 369-376). 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), 25-39. |
| 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) |