ECE 788 – Inference and Learning in Probabilistic Models

Description

Many tasks and applications require a person or an automated system to learn and reason so as to reach conclusions based on the available information. The framework of probabilistic graphical models, reviewed in this course, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. It is becoming a standard tool in a variety of applications, including communications in the presence of noise (e.g., LDPC and turbo decoders), fault and medical diagnosis, genetics, image processing, robot localization, artificial intelligence, etc.

This course covers the three fundamental cornerstones of representation (how to model complex systems with uncertainty?), inference (how to draw conclusions based on evidence?), and learning (how to adjust a model to observations and measurements?) for probabilistic graphical models. In the first part, representation is studied and the two fundamental classes of Bayesian networks and undirected Markov networks are presented in details. Then, in the second part, both exact and approximate inference algorithms are presented, namely variable elimination, message passing, particle-based methods, Monte Carlo methods. Finally, in the third part, learning is discussed by focusing on the problem of learning parameters for Bayesian networks.

Prerequisites

Basic knowledge of probability at the level of ECE 673 is required.

Instructor

Dr. Osvaldo Simeone
Email: osvaldo.simeone@ njit.edu
Phone: (973) 596-5809
Office: 101 FMH Building 
Office Hour: Wednesday 4-6pm

Textbook

Daphne Koller and Nir Friedman, Probabilistic Graphical Models: Principle and Techniques, The MIT Press, 2009 .

Requirements

There will one midterm (40%), and one final exam (40%) and a project (20%) to be completed by the date of the final exam. Weekly problems will be assigned but not graded. Some problem sets might involve Matlab simulation. You can obtain a copy of Matlab software from the campus computing facility. 

For the project, a recent paper will be assigned to each student based on individual interests. Twenty-minute presentations to the class on the selected subject will be scheduled by the end of the semester.

Exams

-         Midterm

-         Final

Fall 2010: Tentative schedule

Week

Topics

Sections covered

Aug 30

Introduction

Review of probability

Conditional probability inference

1.1, 1.2, 1.4, 2.1

Sept 13

Review of graph theory Parametrization of probability distributions

Bayesian networks

2.2, 3.1, 3.2

Sept 20

Independencies in graphs

3.3

Sept 27

From distributions to graphs

3.4

Oct 4

Markov networks

4.1, 4.2

Oct 11

Markov network independencies

4.3

Oct 18

Midterm

Oct 25

Bayesian and Markov networks

4.5

Nov 1

Exact conditional probability inference

Variable elimination

9.2, 9.3, 9.4

Nov 8

Sum-product message passing

10.1, 10.2, 10.3

Nov 15

Inference as optimization

Loopy belief propagation

11.1, 11.2, 11.3, (11.5.1, 11.5.2)

Nov 22

Particle-based approximate inference

12.1, 12.2, 12.3.1-3

Nov 29

Parameter estimation: Maximum likelihood

17.1, 17.2

Dec 6

Parameter estimation: Bayesian estimation

Structure learning

17.3, 17.4, 18.3.1, 18.3.2

Dec 13

Final