Probabilistic Dependency Graphs
This work addresses the problem of representing inconsistent beliefs and improving modularity in graphical models for researchers and practitioners in probabilistic AI.
This paper introduces Probabilistic Dependency Graphs (PDGs), a new class of directed graphical models designed to capture inconsistent beliefs and offer greater modularity than Bayesian Networks (BNs). The authors demonstrate that PDGs can represent BNs and factor graphs, while noting difficulties in representing PDGs with factor graphs.
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.