Event Date
Speaker: Xiucai Ding (Assistant Professor, Statistics, UC Davis)
Title: "Curse of dimensionality and PCA: 20 years on spiked covariance matrix model"
Abstract: This is a survey talk and mainly for random matrix non-experts and graduate students. High dimensional statistics has become one of the central topics in modern statistical theory. In this area, the dimension of the sample is usually divergent with or even larger than the size. Consequently, the classical estimation, inference and decision theory assuming fixed dimensionality usually lose their validity. The main technical reason is that the standard concentration results, like law of large number and central limit theorem usually fail without a substantial modification. To address these issues, random matrix theory has emerged as a particularly useful framework and tool. In this talk, I will explain the curse of dimensionality using principal component analysis. I will make a survey on the existing results and applications based on the simple and famous spiked model. This model was proposed by Iain Johnstone in 2000 and takes us more than 20 years to partially understand it. Open questions will also be discussed.
Seminar date/time: Thursday, October 13, 2022 at 4:10pm
Location: MSB 1147 (Colloquium Room). Refreshments at 3:30pm in MSB Courtyard.