High-Dimensional Statistics credit:

4 Hours

Introduction to the theoretical foundations of high-dimensional statistics, where the number of parameters can be comparable to or larger than the sample size and classical estimators exhibit fundamentally different theoretical behavior. Through examples such as regression and matrix factorization, students develop analytical tools including generalization bounds, convex geometry, replica analysis, leave-one-out techniques, and randomized iterative algorithms, with applications to Bayesian estimation and computational limits of high-dimensional inference. Prerequisite: STAT 510 or STAT 511 , and STAT 527 ; or consent of instructor.