B1187
Title: Marginal independence structures underlying Bayesian networks
Authors: Pratik Misra - KTH Royal Institute of Technology (Sweden) [presenting]
Liam Solus - KTH Royal Institute of Technology (Sweden)
Alex Markham - KTH Royal Institute of Technology (Sweden)
Danai Deligeorgaki - KTH Royal Institute of Technology (Sweden)
Abstract: The problem of estimating the marginal independence structure of a DAG model from observational data is considered. The space of directed acyclic graphs (DAGs) is divided into certain equivalence classes, where each class can be represented by a unique undirected graph called the unconditional dependence graph. The unconditional dependence graphs satisfy certain graphical properties, namely having equal intersection and independence number. Using this observation, a Grobner basis for an associated toric ideal is constructed, and additional binomial relations are defined to connect the space of unconditional dependence graphs. With these moves, a search algorithm, GrUES (Grobner-based Unconditional Equivalence Search), is implemented to estimate the graphical model's conditional independence structure. The implementation shows that GrUES recovers the true marginal independence structure via a BIC-optimal or MAP estimate at a higher rate than simple independence tests while also yielding an estimate of the posterior.
