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Inference in Hybrid Bayesian Networks with Nonlinear Deterministic Conditionals
Author(s) -
Cobb Barry R.,
Shenoy Prakash P.
Publication year - 2017
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21897
Subject(s) - nonlinear system , mathematics , inference , heuristic , bayesian network , algorithm , domain (mathematical analysis) , mathematical optimization , piecewise , bayesian inference , bayesian probability , artificial intelligence , computer science , mathematical analysis , physics , quantum mechanics
To enable inference in hybrid Bayesian networks (BNs) containing nonlinear deterministic conditional distributions, Cobb and Shenoy in 2005 propose approximating nonlinear deterministic functions by piecewise linear (PL) ones. In this paper, we describe a method for finding PL approximations of nonlinear functions based on a penalized mean square error (MSE) heuristic, which consists of minimizing a penalized MSE function subject to two principles, domain and symmetry. We illustrate our method for some commonly used one‐dimensional and two‐dimensional nonlinear deterministic functions such as W = X 2 , W = e X , W = X · Y , and W = X / Y . Finally, we solve two small examples of hybrid BNs containing nonlinear deterministic conditionals that arise in practice.