OR 719 / CSI 775: 
Graphical Models for Inference and Decision Making

Spring 2017

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

Intelligent computer agents must perform goal-directed action in complex, uncertain, and dynamic environments.  Agents tasked with problems of any complexity must have methods for handling uncertainty.  This course examines theory and  methods for building computationally efficient software agents that reason, act and learn in environments characterized by noisy and uncertain information.  The course covers methods based on graphical probability and decision models.  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 independencies 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.


The listed prerequisites are STAT 692 or SYST/STAT 664 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.


Grades will be based on the following:
Assignments 30%
Take-Home Midterm 20%
Take-Home Final 20%
Project 30%


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. Daphne Koller and Nir Friedman. MIT University Press, 2009.

Other recommended texts are:
Modeling and Reasoning with Bayesian Networks. Adnan Darwiche. Cambridge University Press, 2009.
Learning Bayesian Networks. Richard Neapolitan. Prentice Hall, 2003.
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.
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.


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 and obtain free help and support from the instructor and your fellow seminar participants.


Assignments will be posted as they are announced.

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.

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/.

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 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 for Belief Networks - Links to software tools for Bayesian networks
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)
bnlearn - R package for structure learning, parameter learning, and inference
Kevin Murphy's Bayes Net Toolbox - General purpose MATLAB toolbox for Bayesian networks (freeware)
Probabilistic Programming resource page
Primula - Software for Relational Bayesian Networks (freeware)