Statistics and Data Science Seminar

— 5:00pm

Location:
In Person - Posner Hall 153

Speaker:
YANJUN HAN , Assistant Professor of Mathematics and Data Science, Courant Institute of Mathematical Sciences and Center for Data Science, New York University
https://yanjunhan2021.github.io/index.html

Covariance alignment: from MLE to Gromov-Wasserstein

Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment presents significant statistical and computational challenges.

In this talk, I will introduce the covariance alignment model to study and compare various alignment methods and establish a minimax lower bound for covariance alignment that has a non-standard dimension scaling because of the presence of a nuisance parameter. This lower bound is in fact minimax optimal and is achieved by a natural quasi MLE. However, this estimator involves a search over all permutations which is computationally infeasible even when the problem has a moderate size.

To overcome this limitation, I will show that the celebrated Gromov-Wasserstein algorithm from optimal transport which is more amenable to fast implementation even on large-scale problems is also minimax optimal. These results give the first statistical justification for the deployment of the Gromov-Wasserstein algorithm in practice. Finally, I will also discuss the connections to recent literature on statistical graph matching and orthogonal statistical learning.

Based on a joint work with Philippe Rigollet and George Stepaniants.

—

Yanjun Han is an assistant professor of mathematics and data science at the Courant Institute of Mathematical Sciences and the Center for Data Science, New York University. He received his Ph.D. in Electrical Engineering from Stanford University in Aug 2021, under the supervision of Tsachy Weissman. After that, he spent one year as a postdoctoral scholar at the Simons Institute for the Theory of Computing, UC Berkeley, and another year as a Norbert Wiener postdoctoral associate in the Statistics and Data Science Center at MIT, mentored by Sasha Rakhlin and Philippe Rigollet. Honors on his past work include a best student paper finalist at ISIT 2016, a student paper award at ISITA 2016, and the Annals of Statistics Special Invited Session at JSM 2021. His research interests include high-dimensional and nonparametric statistics, bandits, and information theory. 

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