Title

Inference in Hybrid Bayesian Networks with Nonlinear Deterministic Conditionals

Document Type

Article

Publication Date

2017

Abstract

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.

Recommended Citation

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.

DOI for the article

10.1002/int.21897

Department

Marketing

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