Probabilistic Dependency Graphs

Here’s an intriguing generalization of classical graphical model formalisms by Oli Richardson, called Probabilistic Dependency Graphs:

Probabilistic Dependency Graphs (PDGs) are a powerful class of graphical model, that can model the combination of inconsistent beliefs. PDGs generalize Bayesian Networks and Factor graphs, but are arguably more natural to use. This measure of inconsistency is itself quite useful: many information theoretically-motivated notions of loss functions and statistical distances arise naturally as the inconsistencies of the appropriate PDGs. Moreover, relationships between these PDGs give very simple intuitive proofs of otherwise fairly inscrutable results, such as variational bounds, and bounds between statistical distances.

This is a mere placeholder for now. FWIW, the attractions of the PDG framework seem to me very provocative, and I’m especially intrigued by them as a potential formalism for constructing a Generalized Bayesianism by other means than infrabayesianism or ad hoc Bayes by backprop. OTOH they also seem a little bit annoying to compute, so there is more work to be done here.

• orichardson/pdg: probabilistic dependency graph implementation and tools