Lower Bound Bayesian Networks - An Efficient Inference of Lower Bounds on Probability Distributions in Bayesian Networks
This work addresses the challenge of uncertainty quantification in Bayesian networks for researchers and practitioners, offering an incremental improvement by extending existing tools to handle lower bounds more efficiently.
The paper tackles the problem of efficiently inferring lower bounds on probability distributions in Bayesian networks by introducing a method that propagates lower bounds and guarantees outer approximations. The method yields provably exact results for trees with binary variables and competitive approximations for other structures, with superior computational complexity compared to existing approaches.
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.