Seminar Event Detail


Integrable Systems and Random Matrix Theory

Date:  Monday, November 06, 2017
Location:  1866 East Hall (4:00 PM to 5:00 PM)

Title:  A tutorial on Spiked PCA using Linear Spectral Statistics

Abstract:   In this talk we discuss recent work by Edgar Dobriban (2017) that uses linear spectral statistics of eigenvalues of sample covariance matrices to detect the existence of spikes in the regime that the classic spiked models do not have their largest eigenvalues leaving the bulk as in the BBP transition. Here the classic spiked model is where the covariance matrix of the n, p-dimensional random vectors is the identity plus a finite rank perturbation. It is known (Baik, Ben Arous and Peche 2005) in the regime that p/n -> gamma, that for large enough finite perturbation the leading eigenvalue of the sample covariance leaves the bulk of the Marcenko Pastur law (the BBP transition) and therefore can be used as a test for the existence of the finite rank perturbation. As it turns out a test based off of all of the eigenvalues can be more powerful in detecting the existence of the perturbation.

Files:


Speaker:  Asad Lodhia
Institution:  University of Michigan

Event Organizer:   Thomas Bothner and Guilherme Silva    bothner@umich.edu, silvag@umich.edu

 

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