# On Graphical Models and Convex Geometry

arXiv: https://arxiv.org/abs/2106.14255 · HTML: https://mlsanity.com/paper/2106.14255/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2021.

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

- [Deep Adaptation of Adult-Child Facial Expressions by Fusing Landmark Features](https://mlsanity.com/paper/2209.08614/) (2022)
- [Customizable Avatars with Dynamic Facial Action Coded Expressions (CADyFACE) for Improved User Engagement](https://mlsanity.com/paper/2403.07314/) (2024)

## Abstract (arXiv)

We introduce a mixture-model of beta distributions to identify significant correlations among P predictors when P is large. The method relies on theorems in convex geometry, which we use to show how to control the error rate of edge detection in graphical models. Our `betaMix' method does not require any assumptions about the network structure, nor does it assume that the network is sparse. The results in this article hold for a wide class of data generating distributions that include light-tailed and heavy-tailed spherically symmetric distributions.