Many problems in signal processing and statistical inference involve finding sparse
solutions to under-determined, or ill-conditioned, linear systems of equations. A standard …

We propose a new method for estimating parameters in models that are defined by a system
of non-linear differential equations. Such equations represent changes in system outputs by …

This paper studies oracle properties of ℓ 1-penalized least squares in nonparametric
regression setting with random design. We show that the penalized least squares estimator …

Compressive sensing is a new data acquisition technique that aims to measure sparse and
compressible signals at close to their intrinsic information rate rather than their Nyquist rate …

We study high-dimensional generalized linear models and empirical risk minimization using
the Lasso. An oracle inequality is presented, under a so called compatibility condition. Our …

Many statistical machine learning algorithms minimize either an empirical loss function as in
AdaBoost, or a penalized empirical loss as in Lasso or SVM. A single regularization tuning …

Compressive sampling (CS) refers to a generalized sampling paradigm in which
observations are inner products between an unknown signal vector and user-specified test …

In the present paper, we study the problem of aggregation under the squared loss in the
model of regression with deterministic design. We obtain sharp oracle inequalities for …

We introduce MC+, a fast, continuous, nearly unbiased, and accurate method of penalized
variable selection in high-dimensional linear regression. The LASSO is fast and continuous …

The theory of compressive sensing (CS) enables the reconstruction of sparse signals from a
small set of non-adaptive linear measurements by solving a convex l 1 minimization …