光華講壇——社會(huì)名流與企業(yè)家論壇第6719期
主 題：Learning linear non-Gaussian directed acyclic graph: From single to multiple sources學(xué)習(xí)線(xiàn)性非高斯有向無(wú)環(huán)圖：從單個(gè)源到多個(gè)源
主講人：上海財(cái)經(jīng)大學(xué) 賀莘副教授
主持人：統(tǒng)計(jì)學(xué)院 林華珍教授
時(shí)間：1月22日 16:00-17:00
舉辦地點(diǎn)：柳林校區(qū)弘遠(yuǎn)樓408會(huì)議室
主辦單位：統(tǒng)計(jì)研究中心和統(tǒng)計(jì)學(xué)院 科研處
主講人簡(jiǎn)介：
賀莘，上海財(cái)經(jīng)大學(xué)統(tǒng)計(jì)與管理學(xué)院, 副教授。主要研究領(lǐng)域?yàn)榻y(tǒng)計(jì)機(jī)器學(xué)習(xí)及其應(yīng)用，在JASA、JMLR、JCGS、EJS、SINICA、NeurIPS等國(guó)際期刊與會(huì)議上發(fā)表論文20余篇。
內(nèi)容簡(jiǎn)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(wú)環(huán)模型，通常被描述為有向無(wú)環(huán)圖(DAG)，現(xiàn)如今已被廣泛用于表示所收集節(jié)點(diǎn)之間的定向因果關(guān)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(gè)源學(xué)習(xí)線(xiàn)性非高斯DAG的方法，其中的噪聲可以是任何連續(xù)的非高斯分布。該方法利用拓?fù)鋵拥母拍顏?lái)促進(jìn) DAG 學(xué)習(xí)，并在溫和條件下建立了精確恢復(fù) DAG 的理論依據(jù)。特別地，主講人證明了拓?fù)鋵尤绾我宰韵露系姆绞竭M(jìn)行精確重建，并同時(shí)一致地建立節(jié)點(diǎn)之間的因果關(guān)系。此外，主講人還引入了一套新的 DAG 結(jié)構(gòu)相似性度量方法，并提出了一個(gè)轉(zhuǎn)移 DAG 學(xué)習(xí)框架，通過(guò)有效地匯集異構(gòu)數(shù)據(jù)，達(dá)到在目標(biāo)研究中更好地重建 DAG 結(jié)構(gòu)的目的。主講人所建立的漸近 DAG 恢復(fù)方法與許多現(xiàn)有的假定因果忠實(shí)性或噪聲方差有序的學(xué)習(xí)方法形成了鮮明對(duì)比。最后，主講人在各種模擬和實(shí)際應(yīng)用中將這一方法與一些流行的競(jìng)爭(zhēng)方法進(jìn)行了數(shù)值比較，證明了所提方法的優(yōu)勢(shì)。
