Uncertain Bayesian Networks: Learning from Incomplete Data

TL;DR

This paper advances the learning of uncertain Bayesian networks by enabling parameter distribution estimation from incomplete data, improving confidence bounds and inference accuracy.

Contribution

It introduces methods for learning parameter distributions in uncertain Bayesian networks with incomplete data, enhancing existing approaches.

Findings

Improved methods for learning from incomplete data.

Enhanced confidence bounds for Bayesian network queries.

Empirical evaluation demonstrating better performance.

Abstract

When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the probabilities and quantifying the uncertainty in these estimates. We refer to these cases as uncer tain or second-order Bayesian networks. When such data are complete, i.e., all variable values are observed for each instantiation, the conditional probabilities are known to be Dirichlet-distributed. This paper improves the current state-of-the-art approaches for handling uncertain Bayesian networks by enabling them to learn distributions for their parameters, i.e., conditional probabilities, with incomplete data. We extensively evaluate various methods to learn the posterior of the parameters through the desired and empirically derived strength of confidence bounds for various queries.