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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

Lecturer: 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.