Inference in Hybrid Bayesian Networks with Nonlinear Deterministic Conditionals.

This is the peer reviewed version of the following article: Cobb, B. R. and Shenoy, P. P. (2017), Inference in Hybrid Bayesian Networks with Nonlinear Deterministic Conditionals. Int. J. Intell. Syst., 32: 1217–1246. doi:10.1002/int.21897, which has been published in final form at https://doi.org/10.1002/int.21897. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.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 math formula, math formula, math formula, and math formula. Finally, we solve two small examples of hybrid BNs containing nonlinear deterministic conditionals that arise in practice