Related papers: Greedy algorithms: a review and open problems

The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…

In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables…

Considering the set cover problem, by modifying the approach that gives a logarithmic approximation guarantee for the greedy algorithm, we obtain an estimation of the greedy algorithm's accuracy for a particular input. We compare the…

The classical problem of maximizing a submodular function under a matroid constraint is considered. Defining a new measure for the increments made by the greedy algorithm at each step, called the discriminant, improved approximation ratio…

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…

When developing robust preconditioners for multiphysics problems, fractional functions of the Laplace operator often arise and need to be inverted. Rational approximation in the uniform norm can be used to convert inverting those fractional…

Bandit learning is characterized by the tension between long-term exploration and short-term exploitation. However, as has recently been noted, in settings in which the choices of the learning algorithm correspond to important decisions…

This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…

We present new results regarding Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces. We improve earlier bounds in Temlyakov (Forum Math Sigma 2014), for dictionaries satisfying a new…

Many algorithms for maximizing a monotone submodular function subject to a knapsack constraint rely on the natural greedy heuristic. We present a novel refined analysis of this greedy heuristic which enables us to: $(1)$ reduce the…

The "classical" (weak) greedy algorithm is widely used within model order reduction in order to compute a reduced basis in the offline training phase: An a posteriori error estimator is maximized and the snapshot corresponding to the…

We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…

The concept of jump system, introduced by Bouchet and Cunningham (1995), is a set of integer points satisfying a certain exchange property. We consider the minimization of a separable convex function on a jump system. It is known that the…

We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces. The bounds are given only in terms of the upper democracy functions of the basis and its dual. We…

This paper proposes a greedy algorithm named as Big step greedy set cover algorithm to compute approximate minimum set cover. The Big step greedy algorithm, in each step selects p sets such that the union of selected p sets contains…

In the design of algorithms, the greedy paradigm provides a powerful tool for solving efficiently classical computational problems, within the framework of procedural languages. However, expressing these algorithms within the declarative…

We consider a wide class of the discrete optimization problems with interval objective function. We give a generalization of the greedy algorithm for the problems. Using the algorithm, we obtain the set of all possible greedy solutions and…

We discuss the upper and lower estimates for the rate of convergence of Pure and Orthogonal Greedy Algorithms for dictionary with bounded cumulative coherence.

Kernel-based schemes are state-of-the-art techniques for learning by data. In this work we extend some ideas about kernel-based greedy algorithms to exponential-polynomial splines, whose main drawback consists in possible overfitting and…

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…