In random matrix theory, one of the central topics is the limiting behavior of eigenvalues and eigenvectors of random matrices under fixed-rank perturbations. A famous model, raised by Johnstone, is the so-called spiked covariance matrix model. It is a sample covariance matrix whose population has all its eigenvalues equal to one except for a few top eigenvalues (spikes). From the Principal Component Analysis (PCA) point of view, the main task is to study the limiting behavior of the top eigenvalues and eigenvectors of the spiked sample covariance matrix. In practice, the observed matrix may have some data missing, which is a ubiquitous phenomenon in statistics. In this case, the effects of the missing data on principal components of the sample covariance matrix shall be studied, in order to recapture the spikes. In this talk, we will consider the high dimensional setting, namely both the sample size n and the dimension p are large. In the first part, we identify the limiting distribution of the eigenvectors associated with the largest eigenvalues for the sample covariance matrix, under fully general assumptions for spikes, without missing condition. In the second part, we introduce the spiked model with missing condition and discuss the eigenvalue distribution.
15 May 2020
3:30pm - 4:30pm
Where
https://hkust.zoom.us/j/98822781307
Speakers/Performers
Ms. Jingming WANG
HKUST
Organizer(S)
Department of Mathematics
Contact/Enquiries
mathseminar@ust.hk
Payment Details
Audience
Alumni, Faculty and Staff, PG Students, UG Students
Language(s)
English
Other Events
22 Nov 2024
Seminar, Lecture, Talk
IAS / School of Science Joint Lecture - Leveraging Protein Dynamics Memory with Machine Learning to Advance Drug Design: From Antibiotics to Targeted Protein Degradation
Abstract Protein dynamics are fundamental to protein function and encode complex biomolecular mechanisms. Although Markov state models have made it possible to capture long-timescale protein co...
8 Nov 2024
Seminar, Lecture, Talk
IAS / School of Science Joint Lecture - Some Theorems in the Representation Theory of Classical Lie Groups
Abstract After introducing some basic notions in the representation theory of classical Lie groups, the speaker will explain three results in this theory: the multiplicity one theorem for classical...