Matrix Denoising and PCA with Heteroscedastic Noise
I will present recent results on the related problems of denoising, covariance estimation, and principal component analysis for the spiked covariance model with heteroscedastic noise. Specifically, I will present an estimator of the principal components based on whitening the noise, and optimal spectral shrinkers for use with these estimated principal components. I will also show new results on the optimality of whitening for principal subspace estimation. This is joint work with Elad Romanov of the Hebrew University.
William Leeb is an Assistant Professor in the School of Mathematics at the University of Minnesota, Twin Cities. Prior to this, he was a postdoctoral research associate in Amit Singer's research group in the Program in Applied and Computational Mathematics, Princeton University, where he was supported by the Simons Collaboration on Algorithms and Geometry. He completed his Ph.D. in Mathematics in 2015 at Yale University, working under the supervision of Ronald Coifman, and his B.S. in Mathematics in 2010 from the University of Chicago. His research is in applied and computational harmonic analysis, statistical signal processing, and machine learning.