Lower Bound Bayesian Networks - An Efficient Inference of Lower Bounds on Probability Distributions in Bayesian Networks

TL;DR

This paper introduces a new method for propagating lower bounds in Bayesian networks that guarantees outer approximations, is compatible with existing tools, and offers superior computational efficiency across various network structures.

Contribution

A novel method for lower bound propagation in Bayesian networks that guarantees outer bounds, is compatible with existing algorithms, and improves computational efficiency.

Findings

Exact results for trees with binary variables.

Competitive approximations for general network structures.

Superior computational complexity compared to existing methods.

Abstract

We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can use any available algorithms and tools for Bayesian networks in order to represent and infer lower bounds. This new method yields results that are provable exact for trees with binary variables, and results which are competitive to existing approximations in credal networks for all other network structures. Our method is not limited to a specific kind of network structure. Basically, it is also not restricted to a specific kind of inference, but we restrict our analysis to prognostic inference in this article. The computational complexity is superior to that of other existing approaches.