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# Exact Inference on Conditional Linear Γ-Gaussian Bayesian Networks

*Proceedings of the Eighth International Conference on Probabilistic Graphical Models*, PMLR 52:474-486, 2016.

#### Abstract

Exact inference for Bayesian Networks is only possible for quite limited classes of networks. Examples of such classes are discrete networks, conditional linear Gaussian networks, networks using mixtures of truncated exponentials, and networks with densities expressed as truncated polynomials. This paper defines another class with exact inference, based on the normal inverse gamma conjugacy. We describe the theory of this class as well as exemplify our implemented inference algorithm in a practical example. Although generally small and simple, we believe these kinds of networks are potentially quite useful, on their own or in combination with other algorithms and methods for Bayesian Network inference.