A closed-form approach to Bayesian inference in tree-structured graphical models

We propose to learn the structure of an undirected graphical model by computing exact posterior probabilities for local structures in a Bayesian framework. This task would be untractable without any restriction on the considered graphs. We limit our exploration to the spanning trees and define priors on tree structures and parameters that allow fast and exact computation of the posterior probability for an edge to belong to the random tree thanks to an algebraic result called the Matrix-Tree theorem. We show that the assumption we have made does not prevent our approach to perform well on synthetic and flow cytometry data.