Related papers: Some New Convergence Analysis and Applications of …
Sparsity learning with known grouping structure has received considerable attention due to wide modern applications in high-dimensional data analysis. Although advantages of using group information have been well-studied by shrinkage-based…
The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this…
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…
Submodular function maximization finds application in a variety of real-world decision-making problems. However, most existing methods, based on greedy maximization, assume it is computationally feasible to evaluate F, the function being…
The frame algorithm uses a simple recursive formula to approximate an unknown vector from its frame coefficients. This note introduces an adaptive version of the frame algorithm that maximizes the error reduction between steps in terms of…
Greedy methods have recently been successfully applied to generalized kernel interpolation, or the recovery of a function from data stemming from the evaluation of linear functionals, including the approximation of solutions of linear PDEs…
Behavior of the entropy numbers of classes of multivariate functions with mixed smoothness is studied here. This problem has a long history and some fundamental problems in the area are still open. The main goal of this paper is to develop…
In a standard NP-complete optimization problem we introduce an interpolating algorithm between the quick decrease along the gradient (greedy dynamics) and a slow decrease close to the level curves (reluctant dynamics). We find that for a…
Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engineering problems, they have not been shown, theoretically or…
The cosparse analysis model has been introduced recently as an interesting alternative to the standard sparse synthesis approach. A prominent question brought up by this new construction is the analysis pursuit problem -- the need to find a…
We briefly discuss the greedy method and a couple of its more efficient variants for approximately maximizing monotone submodular functions.
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…
This paper focuses on the development of novel greedy techniques for distributed learning under sparsity constraints. Greedy techniques have widely been used in centralized systems due to their low computational requirements and at the same…
We develop and analyze a posteriori error estimators for a proper orthogonal decomposition-discrete empirical interpolation method (Pod-Deim) reduced order model applied to a parametric Poisson equation posed on a parameter-dependent domain…
In this paper we develop the Greedy Recombination Interpolation Method (GRIM) for finding sparse approximations of functions initially given as linear combinations of some (large) number of simpler functions. In a similar spirit to the…
In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a $(2/3)$-approximation for the Maximum Independent Set problem on interval graphs. We show that this is tight, even on unit interval…
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…
We investigate two greedy strategies for finding an approximation to the minimum of a convex function $E$ defined on a Hilbert space $H$. We prove convergence rates for these algorithms under suitable conditions on the objective function…
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…
We present a novel stagewise strategy for improving greedy algorithms for sparse recovery. We demonstrate its efficiency both for synthesis and analysis sparse priors, where in both cases we demonstrate its computational efficiency and…