# Ben Hollering: Toric Ideals of Characteristic Imsets via Quasi-Independence Gluing

**Time: **
Tue 2022-08-30 16.15

**Location: **
3721, Lindstedtsvägen 25, and Zoom

**Video link: **
Meeting ID: 621 8808 6001

**Participating: **
Ben Hollering (MPI Leipzig)

### Abstract

For any directed acyclic graph D, its characteristic imset (CIM) is a 0-1 vector which uniquely encodes the Markov equivalence class of D. To any undirected graph G, the associated characteristic imset polytope CIM(G) is the convex hull of the CIM of each DAG with skeleton G. It was recently shown that many causal discovery algorithms can be viewed as an edge walk on CIM(G). This has led to greater interest in these polytopes and their combinatorial structure.

In this talk, we will instead study these polytopes through the lens of toric geometry. In particular we show that when G is a tree or a cycle, the toric ideal of CIM(G) has a squarefree reduced Grobner basis which can be obtained via a new operation we call quasi-independence gluing.