Inference in Hybrid Bayesian Networks with Nonlinear Deterministic Conditionals
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 urn:x-wiley:08848173:media:int21897:int21897-math-0001, urn:x-wiley:08848173:media:int21897:int21897-math-0002, urn:x-wiley:08848173:media:int21897:int21897-math-0003, and urn:x-wiley:08848173:media:int21897:int21897-math-0004. Finally, we solve two small examples of hybrid BNs containing nonlinear deterministic conditionals that arise in practice.
Cobb, Barry R., and Prakash P. Shenoy. "Inference in Hybrid Bayesian Networks with Nonlinear Deterministic Conditionals." International Journal of Intelligent Systems 32, no. 12 (2017): 1217-1246.
International Journal of Intelligent Systems