Error Estimation in Approximate Bayesian Belief Network Inference
This work addresses error control in approximate inference for Bayesian networks, which is an incremental improvement for researchers and practitioners in probabilistic reasoning.
The paper tackles the problem of estimating the error in approximate Bayesian belief network inference by determining the fraction of high-probability instantiations needed to keep absolute error below a predefined value, using extreme value theory and the reversed generalized Pareto distribution.
We can perform inference in Bayesian belief networks by enumerating instantiations with high probability thus approximating the marginals. In this paper, we present a method for determining the fraction of instantiations that has to be considered such that the absolute error in the marginals does not exceed a predefined value. The method is based on extreme value theory. Essentially, the proposed method uses the reversed generalized Pareto distribution to model probabilities of instantiations below a given threshold. Based on this distribution, an estimate of the maximal absolute error if instantiations with probability smaller than u are disregarded can be made.