Modelling and inference with Conditional Gaussian Probabilistic Decision Graphs

Abstract

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.

A Review of Inference Algorithms for Hybrid Bayesian Networks

“…A convenient feature of PDGs is that any discrete BN can be transformed into a PDG (Jaeger, 2004). It is also known that CLG models can be represented as PDGs (Nielsen, Gámez, & Salmerón, 2012) and therefore inference on such hybrid models can be efficiently performed over them. Recently, it has been shown that MoTBFs can also be represented as PDGs, though so far they have only been tested in practice in supervised classification problems (Fernández, Rumí, del Sagrado, & Salmerón, 2014).…”