Related papers: On Approximation Guarantees for Greedy Low Rank Op…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
We analyze the performance of the greedy algorithm, and also a discrete semi-gradient based algorithm, for maximizing the sum of a suBmodular and suPermodular (BP) function (both of which are non-negative monotone non-decreasing) under two…
This paper concerns a fundamental class of convex matrix optimization problems. It presents the first algorithm that uses optimal storage and provably computes a low-rank approximation of a solution. In particular, when all solutions have…
In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…
The paper gives a systematic study of the approximate versions of three greedy-type algorithms that are widely used in convex optimization. By approximate version we mean the one where some of evaluations are made with an error. Importance…
The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound…
Centrality measures, quantifying the importance of vertices or edges, play a fundamental role in network analysis. To date, triggered by some positive approximability results, a large body of work has been devoted to studying centrality…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
The problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However,…
The rank aggregation problem has received significant recent attention within the computer science community. Its applications today range far beyond the original aim of building metasearch engines to problems in machine learning,…
We present new tight performance guarantees for the greedy maximization of nondecreasing submodular set functions. Our main result first provides a performance guarantee in terms of the overlap of the optimal and greedy solutions. As a…
Let $X=C+\mathrm{E}$ with a deterministic matrix $C\in\R^{M\times M}$ and $\mathrm{E}$ some centered Gaussian $M\times M$-matrix whose entries are independent with variance $\sigma^2$. In the present work, the accuracy of reduced-rank…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…
We study the problem of maximizing a non-negative monotone submodular objective $f$ subject to the intersection of $k$ arbitrary matroid constraints. The natural greedy algorithm guarantees $(k+1)$-approximation for this problem, and the…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this…
For the classical maximum coverage problem, the greedy algorithm achieves a worst-case $1-1/e$ approximation, which is optimal unless $\text{P} = \text{NP}$. The notion of coverage appears in a wide range of optimization tasks, where…
The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically…