Proposal
For my term project, I propose to study Bayesian classification networks. In a
Bayesian network, nodes represent problem parameters, and network topology
encodes probabilistic relationships between these parameters. Inputs correspond
to a priori knowledge which allows inference of posterior probabilities for the
output nodes.
Unfortunately, precise inference of these output values using Bayesian
statistics is an NP-hard problem. To achieve reasonable performance,
approximations must be used. I intend to construct simple framework for
modeling Bayesian networks and use this framework to test a variety of methods
for the inference step on a simple classification problem.
I plan to compare such techniques as Monte Carlo, Markov chaining, and Gaussian
approximation with regard to accuracy, efficiency and generalization. Ideally
this framework will allow for easy visualization of the trade-offs incurred
under each approximation regime. This program will be accompanied by a report
detailing the Bayesian network algorithm and the various inference techniques.