CMSC828X Spring 2019, Advanced Topics in Information Processing:
Algorithms for Probabilistic and Deterministic Graphical Models

The objective of this class is to provide an in-depth 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 message-passing, 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

• 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.

• Introduction: Constraint and probabilistic graphical models.
• Inference in constraints: Adaptive consistency, constraint propagation, arc-conistency.
• Graph properties: induced-width, tree-width, chordal graphs, hypertrees, join-trees.
• Bayesian and Markov networks: Representing independencies by graphs.
• Building Bayesian networks.
• Inference in Probabilistic models: Bucket-elimination (summation and optimization), Tree-decompositions, Join-tree/Junction-tree 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 Mini-bucket, belief-propagation, generalized belief propagation.
• Approximation by Sampling: MCMC schemes, Gibbs sampling, Importance sampling.
• Causal Inference with causal graphs.

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. 1-2	Slides 1
Week 2	2/5	Constraint Network Model	Dechter1 ch. 3 Dechter2 ch. 2-3	Slides 2
	2/7	Inference: Adaptive-Consistency	Dechter2 ch. 2 Montanari paper Numberjack MiniZinc	Slides 3 Problem Set 1
Week 3	2/12	Graph Algorithms, Constraint Propagation		Slides 4
	2/14		Constraint-Propagation (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: Bucket-elimination (Summation, Optimization)	Dechter1 ch. 4 Darwiche ch. 6	Slides 7a Problem Set 3
Week 7	3/12	Probabilistic Inference: Tree-Decomposition (Bucket-Trees, Join-Trees)	Dechter1 ch. 5 Darwiche ch. 7,8	Slides 7b
	3/14
Week 8	3/19	Spring break
	3/21	Spring break
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 Mini-bucket, belief-propagation, generalized belief propagation, variational, cost-shifting methods)	chapter 8:Bounding Inference: Decomposition Bounds	Slides 10
	4/11		chapter 9 Bounding Inference: Iterative Message-Passing
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: Cutset-Sampling	Slides 11b
Week 13	4/23	(no class)
	4/25	Causal Graphical models		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	Final Exam