Class Website Project specification

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
- 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

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)

Discuss the class project

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

Mini-clustering Variational Inference