Solving linear-quadratic conditional Gaussian influence diagrams

This paper considers the problem of solving Bayesian decision problems with a mixture of continuous and discrete variables. We focus on exact evaluation of linear-quadratic conditional Gaussian influence diagrams (LQCG influence diagrams) with additively decomposing utility functions. Based on new and existing representations of probability and utility potentials, we derive a method for solving LQCG influence diagrams based on variable elimination. We show how the computations performed during evaluation of a LQCG influence diagram can be organized in message passing schemes based on Shenoy–Shafer and Lazy propagation. The proposed architectures are the first architectures for efficient exact solution of LQCG influence diagrams exploiting an additively decomposing utility function.