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.
The github repository associated with this page contains some code for those interested in playing with them.
For more information on what these things are and why they’re useful, check out the following papers.
[arXiv]Loss as PDG Inconsistency: choose your model, not your loss (AISTATS 22) [arXiv]
[arXiv]#