This book provides a systematic survey of classical and recent results on hyperbolic cross
approximation. Motivated by numerous applications, the last two decades have seen great …

Consider the high-dimensional linear regression model y= X β*+ w, where y∈\BBR n is an
observation vector, X∈\BBR n× d is a design matrix with d>; n, β*∈\BBR d is an unknown …

Compressed sensing is a new concept in signal processing where one seeks to minimize
the number of measurements to be taken from signals while still retaining the information …

Suppose that we observe entries or, more generally, linear combinations of entries of an
unknown m× T-matrix A corrupted by noise. We are particularly interested in the high …

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This book is a survey on multivariate approximation. The 20th century was a period of
transition from univariate problems to multivariate problems in a number of areas of …

In this note, we address the theoretical properties of Δp, a class of compressed sensing
decoders that rely on ℓp minimization with 0< p< 1 to recover estimates of sparse and …

We determine the exact minimax rate of a Gaussian sequence model under bounded
convex constraints, purely in terms of the local geometry of the given constraint set. Our main …

Let 0< p, q≤∞ and denote by S p N and S q N the corresponding finite-dimensional
Schatten classes. We prove optimal bounds, up to constants only depending on p and q, for …

We propose a simple procedure based on an existing “debiased” l 1-regularized method for
inference of the average partial effects (APEs) in approximately sparse probit and fractional …