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 …

Variables in many big-data settings are structured, arising, for example, from measurements
on a regular grid as in imaging and time series or from spatial-temporal measurements as in …

We consider the problem of sparse estimation in a factor analysis model. A traditional
estimation procedure in use is the following two-step approach: the model is estimated by …

To most applied statisticians, a fitting procedure's degrees of freedom is synonymous with its
model complexity, or its capacity for overfitting to data. In particular, the degrees of freedom …

A generic out-of-sample error estimate is proposed for-estimators regularized with a convex
penalty in high-dimensional linear regression where is observed and the dimension and …

We propose a generalization of the lasso that allows the model coefficients to vary as a
function of a general set of some prespecified modifying variables. These modifiers might be …

We study regularized regression problems where the regularizer is a proper, lower-
semicontinuous, convex and partly smooth function relative to a Riemannian submanifold …

In this article, we consider the nonparametric regression problem with multivariate
predictors. We provide a characterization of the degrees of freedom and divergence for …

Penalized least squares are widely used in signal and image processing. Yet, it suffers from
a major limitation since it requires fine-tuning of the regularization parameters. Under …

The lasso and related sparsity inducing algorithms have been the target of substantial
theoretical and applied research. Correspondingly, many results are known about their …