5 accepted papers
We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and- Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions through “pruning tests”. In standard implementations, evaluatin…
We present a novel screening methodology to safely discard irrelevant nodes within a generic branch-and-bound (BnB) algorithm solving the ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> -penalized least-squares problem. Our contribution is a s…
In this paper, we propose a procedure to accelerate the resolution of the well-known "Elastic-Net" problem. Our procedure is based on the (partial) identification of the solution support and the reformulation of the original problem into a problem of reduced dimension. The identification of the supp…
Antisparse coding aims at spreading the information uniformly over representation coefficients and can be expressed as the solution of an ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -norm regularized problem. In this paper, we propose a ne…
In this work, we present new theoretical results on sparse recovery guarantees for a greedy algorithm, orthogonal matching pursuit (OMP), in the context of continuous parametric dictionaries, i.e., made up of an infinite uncountable number of atoms. We build up a family of dictionaries for which k-s…