講座名稱：Minimal I-maps for margins of Bayesian Networks

講座時間：2020-08-18 16:30

講座人：孫毅 副教授

講座地點：騰訊會議直播（ID：905 459 471）

講座人介紹：

孫毅，新疆大學數(shù)學與系統(tǒng)科學學院副教授、碩士生導師。主要從事圖論、組合論，圖模型與機器學習領(lǐng)域的研究，已在知名期刊The Ramanujan Journal、Theoretical Computer Science等雜志上發(fā)表論文20篇。主持基金8項，其中國家自然科學基金3項，國家博士后基金1項，自治區(qū)基金2項。美國數(shù)學會《數(shù)學評論》評論員。曾為Discrete Mathematics and Theoretical Computer Science 等5個知名期刊多次審稿。

講座內(nèi)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.

主辦單位：數(shù)學與統(tǒng)計學院