# Pratik Misra:Combinatorial and algebraic perspectives on the marginal independence structure of Bayesian networks

**Time: **
Wed 2022-11-30 15.15 - 16.15

**Location: **
KTH 3721

**Video link: **
Zoom meeting ID: 637 4378 6038

**Participating: **
Pratik Misra (KTH)

Abstract: We consider the problem of estimating the marginal independence structure of a Bayesian network from observational data in the form of an undirected graph called the unconditional dependence graph (UDG). In this talk, I will present some graphical properties satisfied by these space of UDGs. Using these properties, we construct a Gröbner basis for a toric ideal associated to the UDGs and define additional combinatorial relations to connect the space of UDGs. In the end, I will talk about a search algorithm called GrUES (Gröbner-based Unconditional Equivalence Search), which we implement on synthetic Gaussian data to recover the true marginal independence structure. This is a joint work with Danai Deligeorgaki, Alex Markham and Liam Solus.