An open toolbox for the reduction, inference computation and sensitivity analysis of Credal Networks

Abstract

Bayesian Networks are a flexible and intuitive tool associated with a robust mathematical background. They have attracted increasing interest in a large variety of applications in different fields. In spite of this, inference in traditional Bayesian Networks is generally limited to only discrete variables or to probabilistic distributions (adopting approximate inference algorithms) that cannot fully capture the epistemic imprecision of the data available. In order to overcome these limitations, Credal Networks have been proposed to integrate Bayesian Networks with imprecise probabilities which, adopting non-probabilistic or hybrid models, allow to fully represent the information available and its uncertainty.Here, a novel computational tool, implemented in the general purpose software OpenCossan, is proposed. The tool provides the reduction of Credal Networks through the use of structural reliability methods, in order to limit the cost associated with the inference computation without impoverishing the quality of the information initially introduced. Novel algorithms for the inference computation of networks involving probability bounds are provided. In addition, a novel sensitivity approach is proposed and implemented into the Toolbox in order to identify the maximum tolerable uncertainty associated with the inputs.