光华讲坛——社会名流与企业家论坛第   期

主 题： An additive graphical model for discrete data

主讲人： 宾夕法尼亚州立大学薛凌洲副教授

主持人：统计学院林华珍教授

时间：2021年12月15日（周三）上午9：30-10：30

直播平台及会议ID：腾讯会议，ID: 333-667-996

主办单位：统计研究中心和统计学院 科研处

主讲人简介：

Lingzhou Xue is an Associate Professor of Statistics at Penn State University. He received B.Sc. in Statistics from Peking University in 2008 and Ph.D. in Statistics from the University of Minnesota in 2012. He was a postdoctoral research associate at Princeton University from 2012-2013. His research interests include high-dimensional statistics, statistical machine learning, optimization, and statistical applications in biological science, business analytics, and geoscience. His research has been supported by National Science Foundation (NSF) and National Institutes of Health (NIH).

薛凌洲，宾夕法尼亚州立大学统计学副教授。2008年获北京大学统计学学士学位，2012年获明尼苏达大学统计学博士学位。2012-2013，他在普林斯顿大学做博士后。他的研究兴趣包括高维统计，统计机器学习，优化算法，和统计在生物科学，商业分析和环境科学等领域的应用。他的研究得到了美国国家科学基金会(NSF)和美国国立卫生研究院(NIH)的支持。

内容提要：

We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional independence by satisfying the semi-graphoid axioms. Based on this relation we build an additive graphical model for discrete variables that does not suffer from the restriction of a parametric model such as the Ising model. We develop an estimator of the new graphical model via the penalized estimation of the discrete version of the additive precision operator and establish the consistency of the estimator under the ultrahigh-dimensional setting. Along with these methodological developments, we also exploit the properties of discrete random variables to uncover a deeper relation between additive conditional independence and conditional independence than previously known. The new graphical model reduces to a conditional independence graphical model under certain sparsity conditions. We conduct simulation experiments and analysis of an HIV antiretroviral therapy data set to compare the new method with existing ones.

我们为基于附加条件独立性的离散节点变量引入了非参数图形模型。加性条件独立是一种三向统计关系，它通过满足半图形公理，与条件独立具有相似的性质。基于这种关系，我们为离散变量构建了一个加性图形模型，该模型不受参数模型（例如 Ising 模型）的限制。我们通过加性精度算子的离散版本的惩罚估计来开发新图形模型的估计器，并在超高维设置下建立估计器的一致性。随着这些方法论的发展，我们还利用离散随机变量的特性来揭示加性条件独立性和条件独立性之间比以前已知的更深的关系。新的图形模型在一定的稀疏条件下简化为条件独立的图形模型。我们对 HIV 抗逆转录病毒治疗数据集进行模拟实验和分析，以将新方法与现有方法进行比较。