Low-rank matrix approximations, such as the truncated singular value decomposition and
the rank-revealing QR decomposition, play a central role in data analysis and scientific …

Conventional wisdom and common practice in acquisition and reconstruction of images from
frequency data follow the basic principle of the Nyquist density sampling theory. This …

This survey describes probabilistic algorithms for linear algebraic computations, such as
factorizing matrices and solving linear systems. It focuses on techniques that have a proven …

High-dimensional probability offers insight into the behavior of random vectors, random
matrices, random subspaces, and objects used to quantify uncertainty in high dimensions …

In this monograph, we have attempted to summarize the actively developing field of
statistical learning with sparsity. A sparse statistical model is one having only a small …

Random matrices now play a role in many areas of theoretical, applied, and computational
mathematics. Therefore, it is desirable to have tools for studying random matrices that are …

This first chapter formulates the objectives of compressive sensing. It introduces the
standard compressive problem studied throughout the book and reveals its ubiquity in many …

Abstract Graph Convolutional Networks (GCNs) are known to suffer from performance
degradation as the number of layers increases, which is usually attributed to over …

A continuing mystery in understanding the empirical success of deep neural networks is
their ability to achieve zero training error and generalize well, even when the training data is …

The purpose of this paper is to propose methodologies for statistical inference of low
dimensional parameters with high dimensional data. We focus on constructing confidence …