Modelling and inference with Conditional Gaussian Probabilistic Decision Graphs

Probabilistic Decision Graphs (PDGs) are probabilistic graphical models that represent a factorisation of a discrete joint probability distribution using a “decision graph”-like structure over local marginal parameters. The structure of a PDG enables the model to capture some context specific independence relations that are not representable in the structure of more commonly used graphical models such as Bayesian networks and Markov networks. This sometimes makes operations in PDGs more efficient than in alternative models. PDGs have previously been defined only in the discrete case, assuming a multinomial joint distribution over the variables in the model. We extend PDGs to incorporate continuous variables, by assuming a Conditional Gaussian (CG) joint distribution. We also show how inference can be carried out in an efficient way.