Propagating moments in probabilistic graphical models for decision support systems

Probabilistic graphical models are widely used to model complex systems with uncertainty. Traditionally, Gaussian directed graphical models are applied for analysis of large networks with continuous variables since they can provide conditional and marginal distributions in closed form simplifying the inferential task. The Gaussianity and linearity assumptions are often adequate, yet can lead to poor performance when dealing with some practical applications. In this paper, we model each variable in graph G as a polynomial regression of its parents to capture complex relationships between individual variables and with utility function of polynomial form. Since the marginal posterior distributions of individual variables can become analytically intractable, we develop a message-passing algorithm to propagate information throughout the network solely using moments which enables the expected utility scores to be calculated exactly. We illustrate how the proposed methodology works in a decision problem in energy systems planning.