Michael's Wiki

Class Website Project specification

• recommended reference 1
• recommended reference 2

Notation

• $I_{PR}(X,Y,Z)$ means “X and Y are independent given Z”.
• $<X,Z,Y>_G$ means “X,Y, and Z are in a graph such that Z separates X from Y.
• “Belief in $x_i$”: posterior marginal on $x_i$ conditioned on all evidence.

Exhaustively enumerating all exceptions in a logical system is intractable. Logic systems have a difficult time handling non-monotonic reasoning. Bayesian logic addresses these issues through explaining away. When evidence is known, we want to update our belief in the system by producing a posterior distribution.

Class outline:

• Graphical models
• Bayesian networks
• Markov networks
• Constraint networks
• inference: Bucket elimination for bayesian and Markov networks
• Dependency graph properties
• Inference: tree decomposition algorithms
• approximation by bounded inference
• Search: AND/OR search spaces
• Approximation by sampling
• Hybrid of search inference
• Learning and Causality

d separation

d separation

Chordal Graphs [http://reasoning.cs.ucla.edu/samiam/ SamIam] [http://en.wikipedia.org/wiki/Bayes_factor Bayes Factor] for soft evidence

Modeling with Bayesian Networks [http://en.wikipedia.org/wiki/Convolution_code Convolutional Codes] (Darwiche 105)

Bucket Elimination

Belief Propagation Inference Finding small induced width

Tree Decomposition Bucket-Tree Elimination Superbuckets

Discuss the class project

Cutset Conditioning Tree Search Spaces Pseudo-Trees

Full OR search trees Context Minimal OR search graph AND-OR Trees Pseudo-Trees

Sampling Importance Sampling

MCMC

Mini-bucket elimination Iterative Bounded Inference

Mini-clustering Variational Inference

Iterative Belief Propagation Iterative Join-graph Propagation

Iterative Join-graph Propagation