Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference

This is joint work with Dr. Zheng Gao.  We will discuss the exact support recovery problem of a high-dimensional sparse signal observed in additive noise.  We will begin by describing the relative stability property for dependent light-tailed error models, which is a type of concentration of maxima phenomenon in extreme value theory.  This phenomenon will be shown to play a key role in the characterization of phase-transitions in the exact support recovery problem.  The phase transition results hold under remarkably wide range of error-dependence structures due to the universality of the concentration of maxima phenomenon.  We illustrate this universality with a characterization of (uniform) relative stability for Gaussian error arrays.

Bio

Dr. Stoev obtained his Ph.D. in Mathematics and Statistics in 2005 from Boston University with Professor Murad S. Taqqu. After graduation, he joined the Department of Statistics at University of Michigan as an Assistant Professor. He was promoted to Associated Professor in 2011 and Professor in 2017. Dr. Stoev’s research interests include stochastic processes and time series, heavy tails and extremes, data intensive applications and computational risk management. See more on his website: https://sites.lsa.umich.edu/sstoev/