5 papers
Resolution-Consistent Greedy Neural Approximation on Infinite-Dimensional Spaces
Pablo M. Berná, Antonio Falcó, Diego Mondéjar
We develop constructive approximation and learning guarantees for shallow neural models with infinite-dimensional inputs observed through finitely many coordinates. The analysis is…
Dictionary-Restricted First-Order Descent Methods: Bounds and Convergence Rates
Miguel Berasategui, Pablo M. Berná, Antonio Falcó
This paper develops a general theory for first-order descent methods whose search directions are restricted to a prescribed dictionary in a reflexive Banach space. Instead of assum…
Step-Size Decay and Structural Stagnation in Greedy Sparse Learning
Pablo M. Berná
Greedy algorithms are central to sparse approximation and stage-wise learning methods such as matching pursuit and boosting. It is known that the Power-Relaxed Greedy Algorithm wit…
Convergence Analysis of Greedy Algorithms with Adaptive Relaxation in Hilbert Spaces
Pablo M. Berná, Andrea GarcÃa
The Power-Relaxed Greedy Algorithm (PRGA) was introduced as a generalization of the so called Relaxed Greedy Algorithm, introduced by DeVore and Temlyakov, by replacing the relaxat…
Maximal inequalities, frames and greedy algorithms
Pablo Berná, Daniel Freeman, Timur Oikhberg +1
The aim of this article is to use Banach lattice techniques to study coordinate systems in function spaces. We begin by proving that the greedy algorithm of a basis is order conver…