For many modern applications in science and engineering, data are collected in a streaming
fashion carrying time-varying information, and practitioners need to process them with a …

The modern strategy for training deep neural networks for classification tasks includes
optimizing the network's weights even after the training error vanishes to further push the …

This is a tutorial on some basic non-asymptotic methods and concepts in random matrix
theory. The reader will learn several tools for the analysis of the extreme singular values of …

We describe a general technique that yields the first Statistical Query lower bounds for a
range of fundamental high-dimensional learning problems involving Gaussian distributions …

Individual neurons often produce highly variable responses over nominally identical trials,
reflecting a mixture of intrinsic 'noise'and systematic changes in the animal's cognitive and …

Random matrix theory is a wide and growing field with a variety of concepts, results, and
techniques and a vast range of applications in mathematics and the related sciences. The …

The classical random matrix theory is mostly focused on asymptotic spectral properties of
random matrices as their dimensions grow to infinity. At the same time many recent …

Structure of this book and how to read it This book is divided into three parts: Part I
Fundamentals, Part II Validation of nominations, Part III Verification of booked capacities …

Random matrices are widely used in sparse recovery problems, and the relevant properties
of matrices with iid entries are well understood. The current paper discusses the recently …

Concentration inequalities form an essential toolkit in the study of high-dimensional
statistical methods. Most of the relevant statistics literature in this regard is, however, based …