相关论文: Lebesgue inequalities for the greedy algorithm in …

Many problems in signal processing and machine learning can be formalized as weak submodular optimization tasks. For such problems, a simple greedy algorithm (\textsc{Greedy}) is guaranteed to find a solution achieving the objective with a…

We propose a randomized greedy search algorithm to find a point estimate for a random partition based on a loss function and posterior Monte Carlo samples. Given the large size and awkward discrete nature of the search space, the…

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…

This research paper addresses the stability of search algorithms in complex networks when dealing with incomplete information or uncertainty. We propose a theoretical model to investigate whether a global search algorithm with incomplete…

Partially greedy bases in Banach spaces were introduced by Dilworth et al. as a strictly weaker notion than the (almost) greedy bases. In this paper, we study two natural ways to strengthen the definition of partial greediness. The first…

Greedy algorithms have long been a workhorse for learning graphical models, and more broadly for learning statistical models with sparse structure. In the context of learning directed acyclic graphs, greedy algorithms are popular despite…

This paper is devoted to the theoretical study of the efficiency, namely, stability of some greedy algorithms. In the greedy approximation theory researchers are mostly interested in the following two important properties of an algorithm --…

In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…

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…

In this effort we introduce and analyze a novel reduced basis approach, used to construct an approximating subspace for a given set of data. Our technique, which we call the Natural Greedy Algorithm (NGA), is based on a recursive approach…

The greedy algorithm adapted from Kruskal's algorithm is an efficient and folklore way to produce a $k$-spanner with girth at least $k+2$. The greedy algorithm has shown to be `existentially optimal', while it's not `universally optimal'…

We study the problem of distributed state estimation in a network of sensing units that can exchange their measurements but the rate of communication between the units is constrained. The units collect noisy, possibly only partial…

The total effective resistance, also called the Kirchhoff index, provides a robustness measure for a graph $G$. We consider two optimization problems of adding $k$ new edges to $G$ such that the resulting graph has minimal total effective…

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 calculate the so-called Rademacher's Grand Lebesgue Space norm for a centered (shifted) indicator (Bernoulli's, binary) random variable. This norm is optimal for the centered and bounded random variables (r.v.). Using this result we…

We extend the classical Lebesgue-Riesz norm estimations for integral operators acting between different classical Lebesgue-Riesz spaces into the Grand Lebesgue Spaces, in the general case. As an example we consider matrix operators acting…

We investigate at decision trees that incorporate both traditional queries based on one attribute and queries based on hypotheses about the values of all attributes. Such decision trees are similar to ones studied in exact learning, where…

In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…

For Schauder bases, Dilworth et al. introduced and characterized the partially greedy property, which is strictly weaker than the (almost) greedy property. Later, Berasategui et al. defined and studied the strong partially greedy property…

We describe an adaptive greedy algorithm for Thiele continued-fraction approximation of a function defined on a continuum domain in the complex plane. The algorithm iteratively selects interpolation nodes from an adaptively refined set of…