Sparse approximate solutions to linear equations are classically obtained via L1 norm
regularized least squares, but this method often underestimates the true solution. As an …

Algorithms for solving variational regularization of ill-posed inverse problems usually involve
operators that depend on a collection of continuous parameters. When the operators enjoy …

In this paper, we consider a class of Forward--Backward (FB) splitting methods that includes
several variants (eg, inertial schemes, FISTA) for minimizing the sum of two proper convex …

Abstract Setting regularization parameters for Lasso-type estimators is notoriously difficult,
though crucial for obtaining the best accuracy. The most popular hyperparameter …

In this manuscript, we study the statistical properties of convex clustering. We establish that
convex clustering is closely related to single linkage hierarchical clustering and k-means …

The discovery of the theory of compressed sensing brought the realisation that many inverse
problems can be solved even when measurements are “incomplete”. This is particularly …

We leverage path differentiability and a recent result on nonsmooth implicit differentiation
calculus to give sufficient conditions ensuring that the solution to a monotone inclusion …

This paper studies well-posedness and parameter sensitivity of the square root LASSO (SR-
LASSO), an optimization model for recovering sparse solutions to linear inverse problems in …

Generalized cross-validation (GCV) is a widely used method for estimating the squared out-
of-sample prediction risk that employs scalar degrees of freedom adjustment (in a …

Abstract The Douglas–Rachford and alternating direction method of multipliers are two
proximal splitting algorithms designed to minimize the sum of two proper lower semi …