The Department of Applied Mathematics weekly seminar is given by scholars and researchers working in applied mathematics, broadly interpreted.
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 data analysis has become one of the central topics in modern statistics and computer science. 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 numbers 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 (PCA). I will make a survey on the existing results based on the famous and simple 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.