Learning linear non-Gaussian directed acyclic graph: From single to multiple sources学习线性非高斯有向无环图：从单个源到多个源

光华讲坛——社会名流与企业家论坛第6719期

主 题：Learning linear non-Gaussian directed acyclic graph: From single to multiple sources学习线性非高斯有向无环图：从单个源到多个源

主讲人：上海财经大学 贺莘副教授

主持人：统计学院 林华珍教授

时间：1月22日 16:00-17:00

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：

贺莘，上海财经大学统计与管理学院, 副教授。主要研究领域为统计机器学习及其应用，在JASA、JMLR、JCGS、EJS、SINICA、NeurIPS等国际期刊与会议上发表论文20余篇。

内容简介：

An acyclic model, often depicted as a directed acyclic graph (DAG), has been widely employed to represent directional causal relations among collected nodes. In this talk, we first propose an efficient method to learn linear non-Gaussian DAG in high dimensional cases from a single source, where the noises can be of any continuous non-Gaussian distribution. The proposed method leverages the concept of topological layer to facilitate the DAG learning, and its theoretical justification in terms of exact DAG recovery is also established under mild conditions. Particularly, we show that the topological layers can be exactly reconstructed in a bottom-up fashion, and the parent-child relations among nodes can also be consistently established. Moreover, we also introduce a novel set of structural similarity measures for DAG and then present a transfer DAG learning framework by effectively pooling the heterogeneous data together for better DAG structure reconstruction in the target study. The established asymptotic DAG recovery is in sharp contrast to that of many existing learning methods assuming parental faithfulness or ordered noise variances. The advantages of the proposed methods are also supported by the numerical comparison against some popular competitors in various simulated examples as well as some real applications.

无环模型，通常被描述为有向无环图(DAG)，现如今已被广泛用于表示所收集节点之间的定向因果关系。本次讲座中，主讲人首先提出了一种在高维情况下从单个源学习线性非高斯DAG的方法，其中的噪声可以是任何连续的非高斯分布。该方法利用拓扑层的概念来促进 DAG 学习，并在温和条件下建立了精确恢复 DAG 的理论依据。特别地，主讲人证明了拓扑层如何以自下而上的方式进行精确重建，并同时一致地建立节点之间的因果关系。此外，主讲人还引入了一套新的 DAG 结构相似性度量方法，并提出了一个转移 DAG 学习框架，通过有效地汇集异构数据，达到在目标研究中更好地重建 DAG 结构的目的。主讲人所建立的渐近 DAG 恢复方法与许多现有的假定因果忠实性或噪声方差有序的学习方法形成了鲜明对比。最后，主讲人在各种模拟和实际应用中将这一方法与一些流行的竞争方法进行了数值比较，证明了所提方法的优势。