# Graphical Models and Exponential Families

arXiv: https://arxiv.org/abs/1301.7376 · HTML: https://mlsanity.com/paper/1301.7376/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2013.

## Built on by (most cited first, 2 of 2)

- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Testing Causal Models with Hidden Variables in Polynomial Delay via Conditional Independencies](https://mlsanity.com/paper/2409.14593/) (2024)

## Abstract (arXiv)

We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks with several families of local distributions, are curved exponential families (CEFs) and graphical models with hidden variables are stratified exponential families (SEFs). An SEF is a finite union of CEFs satisfying a frontier condition. In addition, we illustrate how one can automatically generate independence and non-independence constraints on the distributions over the observable variables implied by a Bayesian network with hidden variables. The relevance of these results for model selection is examined.