Many problems of recent interest in statistics and machine learning can be posed in the
framework of convex optimization. Due to the explosion in size and complexity of modern …

The goal of the sparse approximation problem is to approximate a target signal using a
linear combination of a few elementary signals drawn from a fixed collection. This paper …

Polarization, one of the fundamental properties of light, is critical for certain imaging
applications because it captures information from the scene that cannot directly be recorded …

Many contemporary large-scale applications involve building interpretable models linking a
large set of potential covariates to a response in a non-linear fashion, such as when the …

Best subset selection via a modern optimization lens Page 1 The Annals of Statistics 2016, Vol.
44, No. 2, 813–852 DOI: 10.1214/15-AOS1388 © Institute of Mathematical Statistics, 2016 …

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 …

In many fields of science, we observe a response variable together with a large number of
potential explanatory variables, and would like to be able to discover which variables are …

Fitting high-dimensional statistical models often requires the use of non-linear parameter
estimation procedures. As a consequence, it is generally impossible to obtain an exact …

In the sparse linear regression setting, we consider testing the significance of the predictor
variable that enters the current lasso model, in the sequence of models visited along the …

Compressed sensing (CS) is an emerging field that has attracted considerable research
interest over the past few years. Previous review articles in CS limit their scope to standard …