Experiments with Bayesian Networks Using BNT

Problem
Bayesian network (BN) models, also called graphical models, have emerged as a powerful tool for representing and computing complex probability distributions. A BN factors a probability distribution over a set of random variables into a graph in which missing arcs between nodes (variables) denote conditional independence assumptions. See Kevin Murphy's nice tutorial page for the basics.

BNT is a public domain Matlab toolkit for creating and manipulating Bayesian network models. In this project you will become familiar with the basics of Bayesian networks by using BNT to create some simple models and explore their properties. I expect you to already be familiar with conditional independence, Bayes rule, and the basics of Matlab.

Here is what you need to do.

1. Read the following introductory papers on graphical models:
   • Chpt. 2 "Causal and Bayesian Networks" from Finn Jensen, An Introduction to Bayesian Networks, 1996.
   • Chpt. 2 "Joint Probabilities and Conditional Independence" from Jordan and Bishop, An Introduction to Graphical Models, 2002.
   • Chpt. 3 "The Elimination Algorithm" from An Introduction to Graphical Models.
2. Become familiar with BNT and simple BN models by working through portions of the on-line usage tutorial.
3. Read the following papers describing applications of Bayesian networks to medical diagnosis and computer vision:
   • Speigelhalter et. al. (1993). Bayesian-analysis in expert-systems (with discussion). Statistical Science, 8, 219-283.
   • Rehg et. al. (1999) "Vision-based speaker detection using bayesian networks." In Proc. Conf. on Computer Vision and Pattern Recognition, volume 2, pages 110–116, Ft. Collins, CO, June 1999.
4. Develop several versions of Bayesian network classifiers, starting with Naive Bayes, and apply them to the audio-video dataset from Rehg et. al. and some toy datasets from the UCI machine learning repository.
5. Do some experiments with Bayesian network structure learning (time permitting).

Evaluation

You will write a three page report. It will describe your experiments in part 4 (and 5 if appropriate). You will compare and contrast the performance of different network architectures from both a classification and density estimation perspective.