日時：2024年4月24日(水) 16:10 ~ 18:00

場所：Web（Zoom）（※対象は特に限定しない）

講演者：Marvin Lasserre 先生（Inria Centre, Bordeaux University）

題目： Novel Learning and Inference Methods for Non-Parametric Continuous Bayesian Networks

概要：
Part 1: CMIIC: A Non-Parametric Learning Method for Copula Bayesian Networks
This part of the seminar introduces the concept of Copula Bayesian Networks (CBNs) (G. Elidan, 2010) that leverage copula theory to model relationships between continuous random variables. We present a novel learning algorithm that exploits the graphical language shared between BNs and CBNs, called CMIIC. Moreover, using the empirical Bernstein copula both for conditional independence tests and to estimate copulas from data, we avoid making parametric assumptions, which gives greater generality to our method.

“The Bayesian network (BNs) model is a powerful tool for modeling uncertainty and dependencies between random variables. However, learning and inference in high-dimensional continuous BNs pose significant challenges. Traditional methods often rely on discretization or parametric assumptions, which can lead to inaccuracies, slow computations, or overly constrained models.

Part 2: Inference in Nonparametric Continuous Bayesian Networks
The second part of the seminar focuses on inference in nonparametric continuous BNs. Existing inference methods often rely on discretization or parametric assumptions, leading to limitations. We propose a novel general inference algorithm that avoids these issues.
The algorithm utilizes quadrature rules to compute continuous integrals for exact inference and avoids parametric models by representing the posterior density with orthogonal polynomials. Furthermore, it maintains the efficiency of classical sum-product algorithms through the use of an auxiliary discrete BN specifically constructed for continuous inference.

Keywords: Bayesian networks, copulas, learning, inference, continuous variables, nonparametric, quadrature rules, orthogonal polynomials.”

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dser-center@biwako.shiga-u.ac.jp