光華講壇——社會名流與企業家論壇第6719期

主 題：Learning linear non-Gaussian directed acyclic graph: From single to multiple sources學習線性非高斯有向無環圖：從單個源到多個源

主講人：上海財經大學 賀莘副教授

主持人：統計學院 林華珍教授

時間：1月22日 16:00-17:00

舉辦地點：柳林校區弘遠樓408會議室

主辦單位：統計研究中心和統計學院 科研處

主講人簡介：

賀莘，上海財經大學統計與管理學院, 副教授。主要研究領域為統計機器學習及其應用，在JASA、JMLR、JCGS、EJS、SINICA、NeurIPS等國際期刊與會議上發表論文20余篇。

內容簡介：

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.

無環模型，通常被描述為有向無環圖(DAG)，現如今已被廣泛用于表示所收集節點之間的定向因果關系。本次講座中，主講人首先提出了一種在高維情況下從單個源學習線性非高斯DAG的方法，其中的噪聲可以是任何連續的非高斯分布。該方法利用拓撲層的概念來促進 DAG 學習，并在溫和條件下建立了精確恢復 DAG 的理論依據。特別地，主講人證明了拓撲層如何以自下而上的方式進行精確重建，并同時一致地建立節點之間的因果關系。此外，主講人還引入了一套新的 DAG 結構相似性度量方法，并提出了一個轉移 DAG 學習框架，通過有效地匯集異構數據，達到在目標研究中更好地重建 DAG 結構的目的。主講人所建立的漸近 DAG 恢復方法與許多現有的假定因果忠實性或噪聲方差有序的學習方法形成了鮮明對比。最后，主講人在各種模擬和實際應用中將這一方法與一些流行的競爭方法進行了數值比較，證明了所提方法的優勢。