Theoretical Statistics and Mathematics Unit, ISI Delhi

February 6, 2017 (Monday) ,
3:30 PM at Webinar

Speaker:
Iain Johnstone,
Stanford University

Title:
Low rank structure in highly multivariate models

Abstract of Talk

We start with an overview of some high-dimensional phenomena seen in
principal components analysis. More generally, back in 1964 Alan James
gave a remarkable classification of many of the eigenvalue
distribution problems of multivariate statistics, including PCA. We
show how the classification readily adapts to contemporary `spiked
models' -- high dimensional data with low rank structure. In
particular we approximate likelihood ratios when the number of
variables grows proportionately with sample size or degrees of
freedom. High dimensions bring phase transition phenomena, with quite
different likelihood ratio behavior for small and large spike
strengths. James' framework allows a unified approach to problems
such as signal detection, matrix denoising, regression and canonical
correlations.