**Prof. Tommi S. Jaakkola
tommi@ai.mit.edu**

Course material, howework assignments etc. will be available
on-line

`http://www.ai.mit.edu/courses/6.892-ml`

Weekly assignments will be given each Monday and they are due the following Monday. The level of these assignments will range from short proofs, critiques, or applications to optional research level questions.

A list of papers for class presentations will be made available a bit later in the course.

**Tentative schedule:**

- 1.
**February 3:**Introduction and overview of the course. Problems in machine learning by way of an example. Elements of statistical analysis.- 2.
**February 8:**Elements of graphical models: structured representations of probabilities, graphs, markov properties, decomposable graphs.- 3.
**February 10:**Elements of graphical models cont'd: inference, estimation (ML, MAP, Bayesian).- 4.
**February 15:**Examples of graphical models and their use in density estimation, classification, and clustering.- 5.
**February 17:**Compact representations, statistical physics perspective.- 6.
**February 22:**Graph representations of probabilities more formally. Independence, triangulation, decomposability.- 7.
**February 24:**Formal graph representations cont'd- 8.
**March 1:**Exact inference algorithms: Forward-backward, polytree algorithm, global conditioning.- 9.
**March 3:**Exact inference algorithms cont'd: the junction tree algorithm.- 10.
**March 8:**Inference under limited resources: graph approximations, search based methods.- 11.
**March 10:**Approximate inference and estimation: sampling methods and their combination with exact algorithms.- 12.
**March 15:**Elements of variational methods; mean field and beyond- 13.
**March 17:**Variational methods for graphical models: inference/estimation- 14.
**March 29:**Combination of variational methods with sampling, search, and exact algorithms- 15.
**March 31:**Decision analysis: risk minimization, complexity, uniform convergence.- 16.
**April 5:**Classification/regression: Gaussian process models, support vector machines- 17.
**April 7:**Other kernel based methods. Generalization performance.- 18.
**April 12:**Group theory and invariances.- 19.
**April 14:**Graphical models as domain representations for classification and regression problems.- 20.
**April 21:**Model based clustering from a metric point of view.- 21.
**April 26:**Model selection: graph structure, selection criteria, manifolds, search problems- 22.
**April 28:**Model selection cont'd- 23.
**May 3:**Model averaging: Bayesian, bagging, boosting, and other combination methods. Generalization performance.- 24.
**May 5:**Decision theoretic formulation of graphical models.- 25.
**May 10:**Markov decision problems, reinforcement learning- 26.
**May 12:**Dynamic models e.g. stochastic grammars