OR 719:
Graphical Models for Inference and Decision Making

Spring, 2019
ENGR 1110
Tuesday, 4:30-7:10 PM

This course is dedicated to the memory of journalist Danny Pearl, murdered in February 2002, and to the pioneering research of his father Judea Pearl. Judea Pearl’s research has the potential to create unprecedented advances in our ability to anticipate and prevent future terrorist incidents. May Judea’s research be applied to realize Danny’s vision of a world where people of all cultures live together in peace, harmony, and mutual respect.

Course Description

This course studies methods for drawing inferences and making decisions in environments characterized by uncertainty. In a broad range of applications, from medicine to engineering to robotics to machine learning to policy analysis, there is a need to integrate information from many different sources, about many different uncertain aspects of the world. Graphical probability models were developed for exactly this purpose. A graphical probability model represents both qualititative and quantitative information about the likelihood of different uncertain variables, and about the relationships among different uncertain variables. This course examines theory and methods for computationally efficient algorithms, to reason, learn, and act in environments characterized by noisy and uncertain information. The course studies approaches to representing knowledge about uncertain phenomena, drawing inferences about uncertain phenomena, and planning and acting under uncertainty. Theory, practical tools, and hands-on experience are provided. Students learn graph theoretic concepts for representing conditional dependencies among a set of uncertain hypotheses. Students study exact and approximate methods for updating probabilities to incorporate new information. Practical model building experience is provided. Probabilistic and decision theoretic approaches to major areas of artificial intelligence such as knowledge representation, machine learning, data mining, case-based reasoning, planning, and temporal reasoning are discussed. Students apply what they learn to a semester project of their own choosing.

Prerequisites:

The listed prerequisite is STAT 652 or permission of instructor. Students are expected to have a strong grounding in calculus-based probability theory, to have graduate-level mathematical sophistication, to be competent at building mathematical models and deriving conclusions from the models, to be comfortable performing statistical analysis of a data set and deriving conclusions from the analysis, and to be comfortable with software tools for mathematical modeling such as Matlab, S+, or Mathematica. I will be glad to work with any student to evaluate whether the student's background is appropriate for this course.

Requirements:

Grades will be based on the following:

Assignments 30%
Take-Home Midterm 20%
Take-Home Final 20%
Project 30%

Text:

I teach primarily from notes and do not follow any specific textbook. However, students are strongly encouraged to purchase or borrow a textbook.

Probabilistic Graphical Models: Principles and Techniques (2nd edition) Daphne Koller and Nir Friedman. MIT University Press, 2015.

Other recommended texts are:

Modeling and Reasoning with Bayesian Networks. Adnan Darwiche. Cambridge University Press, 2009.
Bayesian Artificial Intelligence (2nd edition). Kevin Korb and Ann Nicholson. Chapman and Hall, 2010.
Bayesian Networks and Decision Graphs (2nd edition) by Thomas Nielsen and Finn Jensen. Springer, 2007.

Project

The best way to learn something is to apply it. Your project is an excellent opportunity to apply what you are learning to a problem of your own choice.

Assignments

Assignments will be posted as they are announced.

Assignment 1: Due January 29, 2019.
Assignment 2: Due February 5, 2019.
Assignment 3: Due February 12, 2019.
Assignment 4: Due February 19, 2019.
Assignment 5: Due February 26, 2019.
Assignment 6: Due April 2, 2019.
Assignment 7: Due April 16, 2019.

Students are permitted to work together on assignments, but your write-up must be your own. Assignments are intended to provide practical, hands-on experience with the ideas presented in the course. Assignments will be posted on this site. Late assignments receive half credit. The take-home exam must be done individually without collaboration.

Study Aids

From time to time, I post examples and solutions to exercises on Blackboard.

Lecture Notes

Notes from previous years are included here for reference. Updated notes will be posted before class. Classes will be recorded and posted on Blackboard.

If you find these lecture notes helpful and use them in your work, please provide the appropriate citation: Laskey, K.B., Lecture Notes on Computational Models of Probabilistic Inference, Fairfax, VA: George Mason University, http://mason.gmu.edu/~klaskey/GraphicalModels/.

Unit 1: Course Overview and Introduction ** Spring 2019 version**
Unit 2: Graphical Probability Models ** Spring 2019 version**
Unit 3: Representing Knowledge in an Uncertain World ** Spring 2019 version**
Unit 4: Inference in Graphical Models: Propagation in Junction Trees ** Spring 2019 version**
Unit 5: Learning Graphical Models from Observations ** Spring 2019 version**
Unit 6: Inference in Graphical Models: Other Inference Algorithms ** Spring 2019 version**
Unit 7: Inference in Dynamic Bayesian Networks ** Spring 2019 version**
Unit 8: Nonparametric Bayesian Models ** Spring 2019 version**
Unit 9: Knowledge Engineering ** Spring 2019 version**
Unit 10: Graphical Models for Planning and Decision Making ** Spring 2019 version**

Policies and Resources

Useful Links

If you discover broken links, please let me know and I will fix them. Also, I am glad for suggestions of additional useful links.

Organizations, Data Sets and Other Resources
Association for Uncertainty in Artificial Intelligence
Bayesian Network Repository
UCI Machine Learning Repository

Miscellaneous:
Bayesians Worldwide - Links to web pages of Bayesians
Probability Theory: The Logic of Science (classic book by the late E.T. Jaynes)
The Bayesian Songbook (includes Frequentist Frenzy by world renowned songwriter Kathryn Blackmond Laskey)
Software:
Software Packages for Graphical Models - Links to software tools for Bayesian networks
gRaphical Models in R - R packages for representation, inference, learning, and manipulation of graphical probability models
UnBBayes - Open source software for modeling, learning and reasoning with probabilistic graphical models
Netica - Software for Bayesian networks (commercial)
Hugin - Software for Bayesian networks (commercial)
GeNIe & SMILE - Inference and Decision Making Software
SamIam (Sensitivity Analysis, Modeling, Inference and More) - Software for Bayesian networks (freeware)
Kevin Murphy's Bayes Net Toolbox - General purpose MATLAB toolbox for Bayesian networks (freeware; last updated in 2007)
Probabilistic Programming resource page
Primula - Software for Relational Bayesian Networks (freeware)

OR 719: Graphical Models for Inference and Decision Making