| Day | Topic | Reading | Optional Reading | |
| 3/29/10 | Introduction | M. Jordan, "Graphical models," Statistical Science, 19:140-155, 2004. | ||
| 3/31/10 | Semantics of Bayesian networks and Markov random fields | L 2.1.1; P 3 | ||
| 4/05/10 | Computing probabilities: elimination algorithm | |||
| 4/07/10 | Equivalence of chordal graph, decomposability and completeness of minimal separators; Maximum cardinality search algorithm | L 2.1.2-4; P 3.2.4 | R. Tarjan and M. Yannakakis, "Simple linear time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs," SIAM J. Comput., 13(3):566--579, 1984. | |
| 4/12/10 | Heuristics to triangulate a graph; Properties of conditional independence | L 3.1; P 3.1.2-4 | F. Jensen and F. Jensen. "Optimal junction trees," Proceedings of the Tenth Conference Uncertainty and Artificial Intelligence, 360-366, 1994. | |
| 4/14/10 | Markov properties on MRFs | L 3.2.1 | ||
| 4/19/10 | Factorization property on MRFs; Hammersley/Clifford theorem | L 3.2.1 | P. Clifford, "Markov random fields in statistics," In Disorder in Physical Systems, G. Grimmett and D. Welsh (Eds.), 19?2, Oxford University Press, 1990; G. Grimmett, "A theorem about random fields," Bulletin of the London Mathematical Society 5, 81-84, 1973. | |
| 4/21/10 | Markov properties on Bayesian networks | L 3.2.2 | ||
| 4/26/10 | Bayesian networks and directed factorization | |||
| 4/28/10 | Phylogenetic trees and chordal models, mixture Models, inference in HMMs | Phylogenetic trees at Wikipedia | ||
| 5/03/10 | Inference on trees, undirected trees and poly trees | P 4.2-3 | Judea Pearl's classic paper; Belief Propagation at WikiPedia; | |
| 5/05/10 | Exact inference on junction trees | Lauritzen and Spiegelhalter, "Local computation with probabilities on graphical structures and their application to expert systems," J. Roy. Statist. Soc. B, 157?24, 1988. | ||
| 5/10/10 | Message passing protocol and local consistency | |||
| 5/12/10 | Generalized distribution law and Shenoy-Shafer formulation | Aji and McEliece, "The generalized distributive law," IEEE Transactions on Information Theory, 46(2):325-343, 2000; Shafer and Shenoy, "Probability propagation," Annals of Mathematics and Artificial Intelligence, 1:(1-4):327--351, 1990; Kschischang and Frey, "Factor graphs and the sum-product algorithm," IEEE Transactions on Information Theory, 47(2):498-519, 2001 | ||
| 5/17/10 | Computational complexity, time-space complexity tradeoffs | G. Cooper, "The computational complexity of probabilistic inference using Bayesian belief networks," Artificial Intelligence, 42(2-3):393-405, 1990; V. Chandrasekaran, N. Srebro and P. Harsha, "Complexity of inference in graphical models," UAI 2008. | ||
| 5/19/10 | Gaussian graphical models | L 5 | Weiss and Freeman, "Correctness of belief propagation in Gaussian graphical models of arbitrary topology," Neural Computation, 13:2173?200, 2001; Malioutov, Johnson and Willsky, "Walk-sums and belief propagation in Gaussian graphical models," Journal of Machine Learning Research, 7:2031-2064, 2006 | |
| 5/24/10 | Memorial Day Holiday (University Closed) | |||
| 5/26/10 | Structure learning | N. Srebro, "Maximum likelihood bounded tree-width Markov networks," Artificial Intelligence 143(1):123-138, 2003, slides; C. Chow and C. Liu, "Approximating discrete probability distributions with dependence trees," IEEE Transactions on Information Theory, 14(3):462-467, 1968. | ||
| 5/31/10 | Approximate inference: generalized belief propagation, Bethe and Kikuchi free energy, cluster variation method | J. Yedidia, W. Freeman and Y. Weiss, "Constructing free-energy approximations and generalized belief propagation algorithms," IEEE Transactions on Information Theory, 51(7):2282-2312, 2005; M. Wainwright and M. Jordan, "A variational principle for graphical models," In New Directions in Statistical Signal Processing: From Systems to Brain. MIT Press. | ||
| 6/02/10 | ||||
| 6/07/08 | Project presentation |