Quantifying influences in the qualitative probabilistic network with interval probability parameters
A qualitative probabilistic network (QPN) is the qualitative abstraction of a Bayesian network by encoding variables and the qualitative influences between them in a directed acyclic graph. How to quantify the strengths of these influences is critical to resolve trade-offs and avoid ambiguities with conflicting signs during inference, which is hotly debated and studied in recent years. In order to provide for measuring the strengths of qualitative influences and resolving trade-offs, we take interval probability parameters as indicators of influence strengths in this paper. First, we define the conditional interval probabilities and multiplication rules that support causality representation and inference. Then we give the definition of qualitative influences associated with strengths represented by interval probabilities. Further, we propose the corresponding method for inference with the interval-probability-enhanced QPN. By the calculation of interval probabilities, the symmetry and transitivity properties are addressed. By giving a superposition method for qualitative influences associated with strengths, the composition property is interpreted. Building upon these 3 properties, the trade-offs can be well resolved. (C) 2010 Elsevier B.V. All rights reserved.
qualitative probabilistic network interval probability trade-off influence strength inference superposition