Minimal I-maps for margins of Bayesian Networks

讲座名称：Minimal I-maps for margins of Bayesian Networks

讲座时间：2020-08-18 16:30

讲座人：孙毅 副教授

讲座地点：腾讯会议直播（ID：905 459 471）

讲座人介绍：

孙毅，新疆大学数学与系统科学学院副教授、硕士生导师。主要从事图论、组合论，图模型与机器学习领域的研究，已在知名期刊The Ramanujan Journal、Theoretical Computer Science等杂志上发表论文20篇。主持基金8项，其中国家自然科学基金3项，国家博士后基金1项，自治区基金2项。美国数学会《数学评论》评论员。曾为Discrete Mathematics and Theoretical Computer Science 等5个知名期刊多次审稿。

讲座内容：

In this talk, we mainly focus on marginal models which are obtained by marginalizing over a single variable from Bayesian Networks (BNs). We show that there is a minimal I-map for a marginal model of a BN under the condition that a topological order of its model structure is given and then we devise a polynomial time complexity algorithm to find such an I-map.Our solution is based on the theory of directed variable elimination (DVE) method which is proposed by utilizing the relationship between conditional independencies of joint probability distribution and d-separation criterion in BNs. The DVE method is different from the existent variable elimination algorithm because it does not have to moralize the model structure of a BN. Additionally, it is more interpretable in terms of the semantics of BNs since here we no longer regard conditional probability distributions as potential functions. In the end, we touch on the problem on how to find a minimal I-map for marginal models of BNs when we marginalize over multiple variables.

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