Event Date
Speaker: Fan Yang (Postdoctoral Scholar, University of Pennsylvania)
Title: Tracy-Widom law for random Gram matrices
Abstract: Large dimensional random Gram matrices are common objects in high-dimensional statistics and machine learning theory. One of the most important examples is the sample covariance matrix model, whose edge eigenvalues satisfy the famous Tracy-Widom law. On the other hand, for general random Gram matrices with more complicated variance structures, the Tracy-Widom law of their edge eigenvalues are unknown in most settings. These include some important models that have been used in modern statistics, such as the separable covariance matrices, bipartite stochastic block model, and so on. In this talk, I will discuss a new approach to solve this problem by studying the eigenvalue dynamics of a sequence of Gaussian divisible random Gram matrices. Based on this approach, we establish the Tracy-Widom for a general class of spiked random Gram matrices with heteroscedastic variance profiles. With this result, we can construct adaptive, accurate and powerful statistics for some important statistical inference problems, including testing the number of signals, and testing the number of communities in random bipartite networks. Based on the joint work with Xiucai Ding.
About the speaker: Fan Yang is currently a departmental postdoctoral researcher at the University of Pennsylvania. He received his PhD from UCLA. His research interest includes Random Matrix Theory, high dimensional statistics, and statistical learning theory.
Seminar Date/Time: Thursday March 4, 4:10pm
This seminar will be delivered remotely via Zoom. To access the Zoom meeting for this seminar, please contact the instructor Xiucai Ding (xcading@ucdavis.edu) or Pete Scully (pscully@ucdavis.edu) for the meeting ID and password, stating your affiliation.