Event Date
Speaker: Yingying Fan, Professor of Data Sciences and Operations, University of Southern California
Title: "Universal Rank Inference via Residual Subsampling with Application to Large Networks"
Abstract: Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models. In this paper, we suggest a universal approach to rank inference via residual subsampling (RIRS) for testing and estimating rank in a large family of models, including many popularly used network models such as the degree corrected mixed membership model as a special case. Our procedure constructs a test statistic utilizing randomly subsamped entries of the residual matrix constructed by removing the spiked components from the observed data matrix. Our test statistic converges in distribution to the standard normal under the null hypothesis and diverges to infinity with asymptotic probability one under the alternative hypothesis. These results guarantee that the asymptotic size can be controlled at the desired level while achieving asymptotic power one. Our technical analysis is empowered by the asymptotic expansions of eigenvectors and eigenvalues for large random matrices recently developed in Fan, Fan, Han and Lv (2019a, b). The advantages of the newly suggested procedure are the advantages of the newly suggested procedure are demonstrated through several simulation and real data examples. This work is joint with Xiao Han and Qing Yang.
About the speaker: Yingying Fan is current a professor at University of Southern California. She is a fellow of Institute of Mathematical Statistics and American Statistical Association. She is the recipient of many prestigious awards including the Royal Statistical Society Guy Medal in Bronze, the American Statistical Association Noether Young Scholar Award and NSF CAREER Award.
Seminar Date/Time: Thursday February 18, 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.