Matrix Means and a Novel High-dimensional Shrinkage Phenomenon

Abstract: We analyze the impact on covariance estimation of taking a Harmonic mean as opposed to an arithmetic mean of a collection of Wishart Random Matrices in high dimensions. We see that the Harmonic mean improves on the operator norm estimation but curiously does not improve eigenvector recovery as suggested by the Davis-Kahan Inequality. Based on joint work with E. Levina and K. Levin

mathematical physicscombinatoricsprobabilityrepresentation theorystatistics theory

Audience: researchers in the topic

Junior Integrable Probability Seminar

Series comments: The Junior Integrable Probability Seminar is a series of talks taking place online and involving young researchers working in Integrable Probability and related fields. Go to sites.google.com/view/junior-ips for zoom link and password for the talk a day before the seminar.