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Title: Bayesian learning of weakly structural Markov graph laws using sequential Monte Carlo methods Authors:  Felix Rios - The royal institute of technology (Sweden) [presenting]
Abstract: A sequential sampling methodology for weakly structural Markov laws, arising naturally in a Bayesian structure learning context for decomposable graphical models, is presented. As a key component of the suggested approach, we show that the problem of graph estimation, which in general lacks natural sequential interpretation, can be recast into a sequential setting by proposing a recursive Feynman-Kac model that generates a flow of junction tree distributions over a space of increasing dimensions. We focus on particle McMC methods to provide samples on this space, in particular on particle Gibbs (PG), as it allows for generating McMC chains with global moves on an underlying space of decomposable graphs. The suggested sampling methodology is illustrated through numerical examples demonstrating high accuracy in Bayesian graph structure learning in both discrete and continuous graphical models.