DSC 155Hidden Data in Random Matrices
Rigorous treatment of principal component analysis, one of the most effective methods in finding signals amidst the noise of large data arrays. Topics include singular value decomposition for matrices, maximal likelihood estimation, least squares methods, unbiased estimators, random matrices, Wigner’s semicircle law, Markchenko-Pastur laws, universality of eigenvalue statistics, outliers, the BBP transition, applications to community detection, and stochastic block model.