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A logical approach to modelling Boolean Bayesian networks through qualitative information
By Lirong Xia, Yongzhi Cao, and Mingsheng Ying.
Submitted.
Abstract
In this paper, we propose a method to help modelling
a special Bayesian network---Bayesian network with interaction
functions (BNIFs for short). BNIFs are a natural generalization of
many popular models including the causal independence model, and the
most important parameters in a BNIF are interaction functions.
Provided qualitative information by experts, we aim at selecting
interaction functions from candidate sets. To approach this, we
first calculate four qualitative signs for each combination of
candidate interaction functions, then select the combination whose
qualitative signs are mostly suitable for the signs given by
experts. We introduce Boolean deterministic transformation in order
to characterize the signs of four qualitative relations by logical
formulas. These logical formulas drop probabilistic analysis,
therefore provide convenience to calculating qualitative signs. In
addition, we introduce two new qualitative relations, and explore
them with logical formulas in order to increase the precision of the
modelling. We also introduced a technique to significantly simplify
the logical formulas in our method. The approach developed here
gives us an easy and unified way to build BNIFs through qualitative
information.
Paper
Available upon request.