Academic Report of School of Mathematical Sciences [2026] No. 105

(Series Report for High-Level University Construction No. 1364)

Title：Some results on the correlation and conditional graph correlation

Speaker：Researcher Li Qizhai (Chinese Academy of Sciences)

Time：9:00-10:00, Nov. 3, 2026

Location：Tencent Meeting:700666974

Abstract:Inferring the strength of conditional dependence and testing conditional independence are fundamental problems in statistics. A recent breakthrough by Azadkia and Chatterjee intro duced, for the first time, a conditional dependence measure that equals 0 if and only if the variables under study are conditionally independent, and equals 1 if and only if they are conditionally perfectly dependent. They further proposed a computationally efficient and strongly consistent estimator, Tn, based on an ingenious use of ranks and nearest neighbors. Despite these attractive features, the asymptotic theory of Tn has remained largely undeveloped. This paper closes that gap. We prove that, under general dependence, Tn is asymptotically normal and its limiting variance admits a closed form. We also construct consistent variance estimators that are computationally efficient and implementable in O(nlogn) time. Taken together with existing bias-correction methods, these results provide a complete inferential theory for Tn.

Speaker Profile：Li Qizhai is a researcher at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Deputy Director of the Institute of Systems Science. He received his bachelor’s degree from the University of Science and Technology of China in 2001 and his Ph.D. from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, in 2006. From 2006 to 2009, he conducted postdoctoral research at the National Cancer Institute of the National Institutes of Health in the United States. His research interests include biomedical statistics, genetic statistics, and inference from complex data; He has published over 130 academic papers in journals such as Nature Genetics, Science Advances, Angewandte Chemie International Edition, Cancer Research, Microbiome, AJHG, Bioinformatics, IEEE TPMAI, Psychometrika, JASA, and JRSSB; he was elected a Fellow of the American Statistical Association (ASA Fellow, 2020) and an Elected Member of the International Statistical Institute (ISI Elected Member, 2016); Has led or previously led five projects funded by the National Natural Science Foundation of China, including Key Projects, Young Scientists Fund Projects (Category A), Young Scientists Fund Projects (Category B), General Projects, and Young Scientists Fund Projects (Category C); currently serves as Party Secretary and Vice Chairman of the Chinese Society for Field Statistics, and as an Executive Council Member of the Chinese Mathematical Society, among other positions.

Faculty and students are welcome to attend!

Invited by: Zhou Yan

School of Mathematical Sciences

October 29, 2026