L1 regularization, or regularization with an L1 penalty, is a popular idea in statistics and
machine learning. This paper reviews the concept and application of L1 regularization for …

Sparse estimation methods are aimed at using or obtaining parsimonious representations of
data or models. They were first dedicated to linear variable selection but numerous …

A clustering framework within the sparse modeling and dictionary learning setting is
introduced in this work. Instead of searching for the set of centroid that best fit the data, as in …

Submodular functions are relevant to machine learning for at least two reasons:(1) some
problems may be expressed directly as the optimization of submodular functions and (2) the …

Sparse estimation methods are aimed at using or obtaining parsimonious representations of
data or models. While naturally cast as a combinatorial optimization problem, variable or …

Sparse coding consists in representing signals as sparse linear combinations of atoms
selected from a dictionary. We consider an extension of this framework where the atoms are …

The principle of parsimony is central to many areas of science: the simplest explanation of a
given phenomenon should be preferred over more complicated ones. In the context of …

In high dimensional regression settings, sparsity enforcing penalties have proved useful to
regularize the data-fitting term. A recently introduced technique called screening rules …

We consider a class of learning problems that involve a structured sparsity-inducing norm
defined as the sum of $\ell_\infty $-norms over groups of variables. Whereas a lot of effort …

Sparse modeling is a powerful framework for data analysis and processing. Traditionally,
encoding in this framework is performed by solving an l 1-regularized linear regression …