Related papers: The Natural Greedy Algorithm for reduced bases in …
We suggest a new greedy strategy for convex optimization in Banach spaces and prove its convergent rates under a suitable behavior of the modulus of uniform smoothness of the objective function.
We analyze greedy algorithms for the Hierarchical Aggregation (HAG) problem, a strategy introduced in [Jia et al., KDD 2020] for speeding up learning on Graph Neural Networks (GNNs). The idea of HAG is to identify and remove redundancies in…
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 relaxation parameter $1/m$ with $1/m^\alpha$, with the aim of…
The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy…
We propose new algorithms with provable performance for online binary optimization subject to general constraints and in dynamic settings. We consider the subset of problems in which the objective function is submodular. We propose the…
In this paper we study greedy approximation in Banach spaces. We discuss a modification of the Weak Chebyshev Greedy Algorithm, in which steps of the algorithm can be executed imprecisely. Such inaccuracies are represented by both absolute…
We study sparse approximation by greedy algorithms. Our contribution is two-fold. First, we prove exact recovery with high probability of random $K$-sparse signals within $\lceil K(1+\e)\rceil$ iterations of the Orthogonal Matching Pursuit…
We construct two counterexamples that resolve long-standing open problems on greedy approximation theory with respect to bases, posed in [F. Albiac et al., Dissertationes Math. 560 (2021)] and restated in [F. Albiac, J. L. Ansorena, V.…
The study of greedy approximation in the context of convex optimization is becoming a promising research direction as greedy algorithms are actively being employed to construct sparse minimizers for convex functions with respect to given…
We propose a greedy algorithm to select $N$ important features among $P$ input features for a non-linear prediction problem. The features are selected one by one sequentially, in an iterative loss minimization procedure. We use neural…
We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of…
Genetic Algorithms (GA) are a class of metaheuristic global optimization methods inspired by the process of natural selection among individuals in a population. Despite their widespread use, a comprehensive theoretical analysis of these…
Online advertising auctions are fundamental to internet commerce, demanding solutions that not only maximize revenue but also ensure incentive compatibility, high-quality user experience, and real-time efficiency. While recent…
A genetic algorithm (GA) is a search method that optimises a population of solutions by simulating natural evolution. Good solutions reproduce together to create better candidates. The standard GA assumes that any two solutions can mate.…
The purpose of this paper is to introduce $\omega$-Chebyshev-greedy and $\omega$-partially greedy approximation classes and to study their relation with $\omega$-approximation spaces, where the latter are a generalization of the classical…
We provide a communication- and computation-efficient method for distributed submodular optimization in robot mesh networks. Submodularity is a property of diminishing returns that arises in active information gathering such as mapping,…
The goal of this paper is to study the performance of the Thresholding Greedy Algorithm (TGA) when we increase the size of greedy sums by a constant factor $\lambda\geqslant 1$. We introduce the so-called $\lambda$-almost greedy and…
The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems (also known as Markushevich bases) in quasi-Banach spaces from a functional-analytic…
We present convergence estimates of two types of greedy algorithms in terms of the metric entropy of underlying compact sets. In the first part, we measure the error of a standard greedy reduced basis method for parametric PDEs by the…
In this paper, we introduce the neural empirical interpolation method (NEIM), a neural network-based alternative to the discrete empirical interpolation method for reducing the time complexity of computing the nonlinear term in a reduced…