Probabilistic Dependency Graphs

TL;DR

Probabilistic Dependency Graphs (PDGs) are a new flexible class of directed graphical models that better handle inconsistent beliefs and modularity, extending Bayesian Networks and factor graphs with multiple semantics.

Contribution

Introduction of PDGs as a novel class of graphical models with multiple semantics, enhancing modularity and natural representation of inconsistent beliefs.

Findings

PDGs can naturally model inconsistent beliefs.

PDGs extend Bayesian Network semantics.

Factor graphs can be represented as PDGs, but with modeling barriers.

Abstract

We introduce Probabilistic Dependency Graphs (PDGs), a new class of directed graphical models. PDGs can capture inconsistent beliefs in a natural way and are more modular than Bayesian Networks (BNs), in that they make it easier to incorporate new information and restructure the representation. We show by example how PDGs are an especially natural modeling tool. We provide three semantics for PDGs, each of which can be derived from a scoring function (on joint distributions over the variables in the network) that can be viewed as representing a distribution's incompatibility with the PDG. For the PDG corresponding to a BN, this function is uniquely minimized by the distribution the BN represents, showing that PDG semantics extend BN semantics. We show further that factor graphs and their exponential families can also be faithfully represented as PDGs, while there are significant barriers to modeling a PDG with a factor graph.