사업단 소식

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  - 주제 : Nonparametric undirected graphical model selection using diffusion models

  - 초록: An undirected graph represents the unconditional independence structure among random variables.
            Although estimating undirected graphs is important in many applications,
            most existing methods are restricted to parametric settings, such as Gaussian graphical models and Ising models.
            In this talk, we introduce a nonparametric approach to undirected graph estimation based on diffusion models.
            In the first part of the talk, we consider diffusion models as implicit density estimators that adapt to the unknown
            graph structure underlying the data.
            Specifically, we show that diffusion models achieve a near-optimal convergence rate for estimating factorizable
            densities. Despite this desirable property, however, diffusion models do not directly provide an explicit estimator
            of the underlying graph.
            To address this limitation, we propose a novel method for nonparametric undirected graphical model selection that does not rely on parametric assumptions.
            Furthermore, we demonstrate that the proposed method can consistently recover the true underlying graph.