# Probabilistic Dependency Graphs

arXiv: https://arxiv.org/abs/2012.10800 · HTML: https://mlsanity.com/paper/2012.10800/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2020.

## Built on by (most cited first, 3 of 3)

- [Loss as the Inconsistency of a Probabilistic Dependency Graph: Choose Your Model, Not Your Loss Function](https://mlsanity.com/paper/2202.11862/) (2022)
- [Inference for Probabilistic Dependency Graphs](https://mlsanity.com/paper/2311.05580/) (2023)
- [Learning with Confidence](https://mlsanity.com/paper/2508.11037/) (2025)

## Abstract (arXiv)

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.