光华讲坛——社会名流与企业家论坛第 期
主 题:Gaussian Chain Graph: Identifiability, Estimation and Asymptotics
主讲人:香港中文大学张浩然博士
主持人:统计学院林华珍教授
时间:2023年5月16日(周二)下午15:00-16:00
举办地点:柳林校区弘远楼408会议室
主办单位:统计研究中心和统计学院 科研处
主讲人简介:
张浩然博士现任香港中文大学统计系博士后,将于2023年8月加入南方科技大学统计与数据科学系担任助理教授。其分别于2016年和2021年在复旦大学取得学士(数学与应用数学)和博士(统计学)学位,师从应志良教授,2017-2019年获得国家留学基金委资助在哥伦比亚大学统计系访问。其主要从事统计机器学习,网络和图模型,以及计量心理学研究,在Journal of Machine Learning Research,Psychometrika等期刊发表多篇文章,并担任 Statistica Sinica,Journal of Computational and Graphical Statistics 等统计学期刊,Psychometrika 等计量心理学期刊的匿名审稿人。
内容简介:
The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently encountered in practice, the chain graph model has been largely under investigated in literature, possibly due to the lack of identifiability conditions between undirected and directed edges. In this paper, we first establish a set of novel identifiability conditions for the Gaussian chain graph model, exploiting a low rank plus sparse decomposition of the precision matrix. Further, an efficient learning algorithm is built upon the identifiability conditions to fully recover the chain graph structure. Theoretical analysis on the proposed method is conducted, assuring its asymptotic consistency in recover- ing the exact chain graph structure. The advantage of the proposed method is also supported by numerical experiments on both simulated examples and a real application on the Standard & Poor 500 index data.
链图模型是一类广义的图模型,其允许在一个图中同时存在无向边和有向边,其中节点之间对称的条件相关性通过无向边编码,而非对称的因果相关性通过有向边编码。链图模型在金融,生物以及社会科学等领域中有着广泛的应用,但现有文献对其研究并不充分,其原因在于缺乏区分无向边和有向边的可识别条件。本文利用精度矩阵的低秩加稀疏分解,建立了高斯链图模型的一组新的可识别条件,并在此基础上,建立了一种链图结构学习算法,用于重建链图结构。我们对该算法进行了理论分析,证明了其统计相合性。据主讲人所知,这是文献中第一个链图精确结构的渐近相合估计。主讲人应用此算法分析标普500股票数据,其结果精确区分了不同股票之间的条件相关性和因果相关性,并且显示了新冠疫情对于不同行业造成了不同程度的打击。