Summarizing the effect of many covariates through a few linear combinations is an effective
way of reducing covariate dimension and is the backbone of (sufficient) dimension …

L1 regularization, or regularization with an L1 penalty, is a popular idea in statistics and
machine learning. This paper reviews the concept and application of L1 regularization for …

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 …

Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional
random vectors Page 1 The Annals of Statistics 2013, Vol. 41, No. 6, 2786–2819 DOI …

The compressive sensing (CS) framework aims to ease the burden on analog-to-digital
converters (ADCs) by reducing the sampling rate required to acquire and stably recover …

Supplementary material for Least squares after model selection in high-dimensional sparse
models. The online supplemental article 2 contains a finite sample results for the estimation …

We give the first computationally tractable and almost optimal solution to the problem of one‐
bit compressed sensing, showing how to accurately recover an s‐sparse vector\input …

After a decade of extensive study of the sparse representation synthesis model, we can
safely say that this is a mature and stable field, with clear theoretical foundations, and …

This paper considers compressed sensing and affine rank minimization in both noiseless
and noisy cases and establishes sharp restricted isometry conditions for sparse signal and …

We propose a method for constructing p-values for general hypotheses in a high-
dimensional linear model. The hypotheses can be local for testing a single regression …