Related papers: Subset selection for matrices by column exchange
Spatio-temporal hidden Markov models are extremely difficult to estimate because their latent joint distributions are available only in trivial cases. In the estimation phase, these latent distributions are usually substituted with…
In a model of network communication based on a random walk in an undirected graph, what subset of nodes (subject to constraints on the set size), enable the fastest spread of information? The dynamics of spread is described by a process…
We address the problems of minimizing and of maximizing the spectral radius overa compact family of non-negative matrices. Those problems being hard in generalcan be efficiently solved for some special families. We consider the so-called…
In this short note we prove a lemma about the dimension of certain algebraic sets of matrices. This result is needed in our paper arXiv:1201.1672. The result presented here has also applications in other situations and so it should appear…
Matrix recovery is the problem of recovering a low-rank matrix from a few linear measurements. Recently, this problem has gained a lot of attention as it is employed in many applications such as Netflix prize problem, seismic data…
Given a set of $n$ vectors in $\mathbb{R}^d$, the goal of the \emph{determinant maximization} problem is to pick $k$ vectors with the maximum volume. Determinant maximization is the MAP-inference task for determinantal point processes (DPP)…
We explore the problem of approximate matrix multiplication (AMM) within the sliding window model, where algorithms utilize limited space to perform large-scale matrix multiplication in a streaming manner. This model has garnered increasing…
Many robotic systems deal with uncertainty by performing a sequence of information gathering actions. In this work, we focus on the problem of efficiently constructing such a sequence by drawing an explicit connection to submodularity.…
We study mechanisms that use greedy allocation rules and pay-your-bid pricing to allocate resources subject to a matroid constraint. We show that all such mechanisms obtain a constant fraction of the optimal welfare at any equilibrium of…
We consider a distributed resource allocation problem in networks where each transmitter-receiver pair aims at maximizing its local utility function by adjusting its action matrix, which belongs to a given feasible set. This problem has…
We propose a class of subspace ascent methods for computing optimal approximate designs that covers both existing as well as new and more efficient algorithms. Within this class of methods, we construct a simple, randomized exchange…
Random search processes are instrumental in studying and understanding navigation properties of complex networks, food search strategies of animals, diffusion control of molecular processes in biological cells, and improving web search…
We study the low rank approximation problem of any given matrix $A$ over $\mathbb{R}^{n\times m}$ and $\mathbb{C}^{n\times m}$ in entry-wise $\ell_p$ loss, that is, finding a rank-$k$ matrix $X$ such that $\|A-X\|_p$ is minimized. Unlike…
We consider a cross interpolation of high-dimensional arrays in the tensor train format. We prove that the maximum-volume choice of the interpolation sets provides the quasioptimal interpolation accuracy, that differs from the best possible…
We consider the celebrated bound introduced by Conforti and Cornu\'ejols (1984) for greedy schemes in submodular optimization. The bound assumes a submodular function defined on a collection of sets forming a matroid and is based on greedy…
Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is…
Ranking and selection (R&S) aims to select the best alternative with the largest mean performance from a finite set of alternatives. Recently, considerable attention has turned towards the large-scale R&S problem which involves a large…
In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and…
We study an elementary path problem which appears in the pricing step of a column generation scheme solving the kidney exchange problem. The latter aims at finding exchanges of donations in a pool of patients and donors of kidney…
We study the problem of optimal traffic prediction and monitoring in large-scale networks. Our goal is to determine which subset of K links to monitor in order to "best" predict the traffic on the remaining links in the network. We consider…