Related papers: On Greedy Algorithms with bounded cumulative coher…
In many prediction problems, it is not uncommon that the number of variables used to construct a forecast is of the same order of magnitude as the sample size, if not larger. We then face the problem of constructing a prediction in the…
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 Kaczmarz method is an iterative algorithm for solving systems of linear equalities and inequalities, that iteratively projects onto these constraints. Recently, Strohmer and Vershynin [J. Fourier Anal. Appl., 15(2):262-278, 2009] gave a…
Nearly three decades ago, Bar-Noy, Motwani and Naor showed that no online edge-coloring algorithm can edge color a graph optimally. Indeed, their work, titled "the greedy algorithm is optimal for on-line edge coloring", shows that the…
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 the convergence of generalized kernel-based interpolation methods. This is done under minimalistic assumptions on both the kernel and the target function. On these grounds, we further prove convergence of popular greedy data…
We study the fundamental limits of matching pursuit, or the pure greedy algorithm, for approximating a target function $ f $ by a linear combination $f_n$ of $n$ elements from a dictionary. When the target function is contained in the…
Sparse approximation is important in many applications because of concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is…
This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards)…
Chebyshev Greedy Algorithm is a generalization of the well known Orthogonal Matching Pursuit defined in a Hilbert space to the case of Banach spaces. We apply this algorithm for constructing sparse approximate solutions (with respect to a…
More precise estimation of the greedy algorithm complexity for a special case of the set cover problem is given in this paper.
Motivated by sequential budgeted allocation problems, we investigate online matching problems where connections between vertices are not i.i.d., but they have fixed degree distributions -- the so-called configuration model. We estimate the…
Kernel-based methods provide flexible and accurate algorithms for the reconstruction of functions from meshless samples. A major question in the use of such methods is the influence of the samples locations on the behavior of 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…
Data-dependent greedy algorithms in kernel spaces are known to provide fast converging interpolants, while being extremely easy to implement and efficient to run. Despite this experimental evidence, no detailed theory has yet been…
Orthogonal greedy learning (OGL) is a stepwise learning scheme that starts with selecting a new atom from a specified dictionary via the steepest gradient descent (SGD) and then builds the estimator through orthogonal projection. In this…
Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space $X$. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper…
A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…
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…
We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant degree regular graphs. We show that for $r$-regular graphs with $n$ nodes and girth at least $g$, the…