Lecture
Days: Tuesday/Thursday
Time: 3:30 pm  4:45 pm
Room: CSI 3120
Instructor: Rina Dechter
Office hours: Monday 11:30 am  12:30 pm (3219 AVW)
Course Description
The objective of this class is to provide an indepth exposition of representation and reasoning under uncertainty using
the framework of Graphical models. The class focuses on reasoning with uncertainty using directed and undirected
graphical models such as Bayesian networks, Markov networks and constraint networks. These graphical models encode
knowledge as probabilistic relations among variables. The primary reasoning tasks are, given some observations, to find
the most likely scenario over a subset of propositions, or to update the degree of belief (distribution) over a subset
of the variables. The primary algorithms (exact and approximate) using variational messagepassing, search and sampling
will be covered, with illustrations from areas such as bioinformatics, diagnosis and planning. Additional topics may
include: causal networks, and dynamic decision networks (Influence diagrams and MDPS), as time permits.
Requirements
In this class I will teach the algorithmic principles that allow reasoning and learning for graphical models. Students
will have 5 problems set of homeworkâs (50%) and a project (20%) that include presenting recent papers in the area. There will be a final
(30%).
Prerequisites
 Familiarity with basic concepts of probability theory.
 Knowledge of basic computer science, algorithms and programming principles.
 Previous exposure to AI is desirable but not essential.
Course material
The course will be based mostly on four sources:
Additional sources:
Some links to software and tools.
Course Topics
 Introduction: Constraint and probabilistic graphical models.
 Inference in constraints: Adaptive consistency, constraint propagation, arcconistency.
 Graph properties: inducedwidth, treewidth, chordal graphs, hypertrees, jointrees.
 Bayesian and Markov networks: Representing independencies by graphs.
 Building Bayesian networks.
 Inference in Probabilistic models: Bucketelimination (summation and optimization), Treedecompositions, Jointree/Junctiontree algorithm.
 Search in CSPs: Backtracking, pruning by constraint propagation, backjumping and learning.
 Search in Graphical models: AND/OR search Spaces for likelihood, optimization queries.
 Approximate Bounded Inference: weighted Minibucket, beliefpropagation, generalized belief propagation.
 Approximation by Sampling: MCMC schemes, Gibbs sampling, Importance sampling.
 Causal Inference with causal graphs.
Schedule
Week 
Date 
Topic 
Readings / Resoures 
Slides / HW 
Week 1 
1/29 
(class canceled due to weather)




1/31 
 Introduction: Constraint and Probabilistic Graphical Models

Dechter1 ch. 12

Slides 1

Week 2 
2/5 

Dechter1 ch. 3
Dechter2 ch. 23

Slides 2


2/7 
 Inference: AdaptiveConsistency

Dechter2 ch. 2
Montanari paper
Numberjack
MiniZinc

Slides 3
Problem Set 1

Week 3 
2/12 
 Graph Algorithms, Constraint Propagation


Slides 4


2/14 

ConstraintPropagation (Bessiere)
Chapter3  Constraints


Week 4 
2/19 
 Bayesian and Markov networks: Representing independencies by graphs

Darwiche ch. 4

Slides 5


2/21 


Problem Set 2

Week 5 
2/26 




2/28 
 Building Bayesian Networks

Darwiche ch. 5

Slides 6

Week 6 
3/5 




3/7 
 Probabilistic Inference: Bucketelimination (Summation, Optimization)

Dechter1 ch. 4
Darwiche ch. 6

Slides 7a
Problem Set 3

Week 7 
3/12 
 Probabilistic Inference: TreeDecomposition (BucketTrees, JoinTrees)

Dechter1 ch. 5
Darwiche ch. 7,8

Slides 7b


3/14 



Week 8 
3/19 




3/21 



Week 9 
3/26 
 Backtracking search for CSPs

Dechter2 ch. 5,6

Slides 8


3/28 


Problem Set 4

Week 10 
4/2 
 Search: AND/OR search Spaces for likelihood, optimization queries
(Probability of evidence, Partition function, MAP and MPE queries)

Dechter1 ch. 6

Slides 9


4/4 



Week 11 
4/9 
 Bounded Inference: weighted Minibucket, beliefpropagation, generalized belief propagation, variational, costshifting methods)

chapter 8:Bounding Inference: Decomposition Bounds

Slides 10


4/11 

chapter 9 Bounding Inference: Iterative MessagePassing


Week 12 
4/16 
 Sampling: MCMC methods for graphical models: Importance sampling and Gibbs sampling schemes


Slides 11a
Problem Set 5


4/18 

Darwiche ch. 15
Paper: CutsetSampling

Slides 11b

Week 13 
4/23 




4/25 


Slides 12

Week 14 
4/30 




5/2 
 Guest Speaker: Joshua Brule on Causal Programming


Slides

Week 15 
5/7 




5/9 



Week 16 
5/14 



Week 17 
5/22 



 Software Links

 Numberjack  A Python platform for Combinatorial Optimisation
 MiniZinc  Modeling Language
 UnBBayes  Modeling, Learning and Reasoning upon Probabilistic Networks
