報告人：許王莉 教授
報告題目：Differentially Private Joint Independence Test
報告時間：2026年5月21日（周四）下午3：00
報告地點：云龍校區6號樓304報告廳
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
許王莉：2006年畢業于中國科學院數學與系統科學研究院應用所概率論與數理統計專業，目前是中國現場統計研究會生存分析分會副秘書長、國際生物統計學會中國分（IBS-CHINA）青年理事，眾多國內外統計學術期刊的審稿專家，現任中國人民大學書院建設與管理中心副主任、明理書院副院長、統計學教授。近年來一直從事模型擬合優度檢驗，高維數據分析，隨機缺失數據，兩階段抽樣數據以及縱向數據分析等方面的統計推斷研究。先后承擔了“新世紀優秀人才計劃”，“北京市科技新星計劃”，國家自然科學面上基金，國家自然科學青年基金和教育部人文社科基金等多項科研課題，在統計學國際一流期刊發表論文40余篇，并在科學出版社合作出版《非參數蒙特卡洛檢驗及其應用》和單著《缺失數據的模型檢驗及其應用》。
報告摘要：
Identification of joint dependence among more than two random vectors plays an important role in many statistical applications, where the data may contain sensitive or confidential information. In this paper, we consider the d-variable Hilbert-Schmidt independence criterion (dHSIC) in the context of differential privacy. Given that the limiting distribution of the empirical estimate of dHSIC is a complicated Gaussian chaos, constructing tests in the non-private regime is typically based on permutation and bootstrap methods. To detect joint dependence in privacy, we propose a dHSIC-based testing procedure by employing a differentially private permutation methodology. Our method enjoys privacy guarantee, valid level and pointwise consistency, while the bootstrap counterpart suffers from inconsistent power. We further investigate the uniform power of the proposed test in dHSIC metric and L2 metric, indicating that the proposed test attains the minimax optimal power across different privacy regimes. As a byproduct, our results also establish the pointwise and uniform power of the non-private permutation dHSIC, addressing an unsolved question remained in Pfister(2018). Both numerical simulations and real data analysis in causal inference suggest our proposed test performs well empirically.