Related papers: Greedy Algorithms for Reduced Bases in Banach Spac…
We consider the problem of studying the performance of greedy algorithm on sensor selection problem for stable linear systems with Kalman Filter. Specifically, the objective is to find the system parameters that affects the performance of…
We present a general approximation framework for weighted integer covering problems. In a weighted integer covering problem, the goal is to determine a non-negative integer solution $x$ to system $\{ Ax \geq r \}$ minimizing a non-negative…
Despite the great success of deep learning, recent works show that large deep neural networks are often highly redundant and can be significantly reduced in size. However, the theoretical question of how much we can prune a neural network…
Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms…
This article closes the cycle of characterizations of greedy-like bases in the isometric case initiated in [F. Albiac and P. Wojtaszczyk, Characterization of $1$-greedy bases, J. Approx. Theory 138 (2006)] with the characterization of…
We study sublinear time algorithms for estimating the size of maximum matching in graphs. Our main result is a $(\frac{1}{2}+\Omega(1))$-approximation algorithm which can be implemented in $O(n^{1+\epsilon})$ time, where $n$ is the number…
We analyze the orthogonal greedy algorithm when applied to dictionaries $\mathbb{D}$ whose convex hull has small entropy. We show that if the metric entropy of the convex hull of $\mathbb{D}$ decays at a rate of $O(n^{-\frac{1}{2}-\alpha})$…
Consider two ordered positive real number arrays of equal size. The problem is to find such set of indices of given size that the ratio of the sums of the array elements with those indices is minimized. In this work, in order to mitigate…
We study the problem of improving the greedy constant or the democracy constant of a basis of a Banach space by renorming. We prove that every Banach space with a greedy basis can be renormed, for a given $\vare>0$, so that the basis…
Performing inference in Bayesian models requires sampling algorithms to draw samples from the posterior. This becomes prohibitively expensive as the size of data sets increase. Constructing approximations to the posterior which are cheap to…
We study the properties of a simple greedy algorithm for the generation of data-adapted anisotropic triangulations. Given a function f, the algorithm produces nested triangulations and corresponding piecewise polynomial approximations of f.…
It is known that for a conditional quasi-greedy basis $\mathcal{B}$ in a Banach space $\mathbb{X}$, the associated sequence $(k_{m}[\mathcal{B}])_{m=1}^{\infty}$ of its conditionality constants verifies the estimate…
Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…
We consider learning a convex combination of basis models, and present some new theoretical and empirical results that demonstrate the effectiveness of a greedy approach. Theoretically, we first consider whether we can use linear, instead…
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…
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'…
Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent…
Randomized greedy algorithms form one of the simplest yet most effective approaches for computing approximate matchings in graphs. In this paper, we focus on the class of vertex-iterative (VI) randomized greedy matching algorithms, which…
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…
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…