Practical Aspects of Solving Hybrid Bayesian Networks Containing Deterministic Conditionals

AbstractIn this paper, we discuss some practical issues that arise in solving hybrid Bayesian networks that include deterministic conditionals for continuous variables. We show how exact inference can become intractable even for small networks due to the difficulty in handling deterministic conditionals for continuous variables. We propose some strategies for carrying out the inference task using mixtures of polynomials MOPs and mixtures of truncated exponentials. MOPs can be defined on hypercubes or hyperrhombuses. We compare these two methods. A key strategy is to reapproximate large potentials with potentials consisting of fewer pieces and lower degrees/number of terms. We discuss several methods for reapproximating potentials. We illustrate our methods in a practical application consisting of solving a stochastic program evaluation and review technique PERT network.