CS 281A / Stat 241A, Spring 2007:

Statistical Learning Theory

Course description

This course will provide an introduction to probabilistic and computational methods for the statistical modeling of complex, multivariate data. It will concentrate on graphical models, and in particular issues of representation, estimation, and inference in parametric models.

Outline:

Introduction to graphical models.
Conditional independence. Directed and undirected graphical models.
Inference:

Elimination algorithm.
Sum-product algorithm.
Factor graphs.

Estimation and parameterization:

Bayesian, MAP, ML estimation.
Linear regression.
Linear classification.
Exponential family. Conjugacy.
Sufficient statistics. ML estimation.
The EM algorithm.

Examples:

HMMs.
Factor analysis.
Kalman filter.

General inference algorithms:

Junction tree.
Approximate inference: sampling methods.
Approximate inference: variational methods.

Prerequisites:

The prerequisites are previous coursework in linear algebra, multivariate calculus, and basic probability and statistics. Previous coursework in graph theory, information theory and optimization theory would be helpful but is not required. Familiarity with Matlab, Splus or a related matrix-oriented programming language will be necessary.

Text book:

The course will follow the unpublished manuscript An Introduction to Probabilistic Graphical Models, by Michael I. Jordan, which will soon be available from Copy Central at 2483 Hearst Avenue. For an introduction, see the review paper Michael I. Jordan, Graphical models. .

mailto:bartlett@cs