Related papers: Superfast 1-Norm Estimation
We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…
We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the…
We consider sparse matrix estimation where the goal is to estimate an $n\times n$ matrix from noisy observations of a small subset of its entries. We analyze the estimation error of the popularly utilized collaborative filtering algorithm…
Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…
Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…
Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well…
We present a novel algorithm attaining excessively fast, the sought solution of linear systems of equations. The algorithm is short in its basic formulation and, by definition, vectorized, while the memory allocation demands are trivial,…
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…
A growing number of problems in computational mathematics can be reduced to the solution of many linear systems that are related, often depending smoothly or slowly on a parameter $p$, that is, $A(p)x(p)=b(p)$. We introduce an efficient…
In this paper we discuss a well known computing problem -- inference for models with intractable normalizing functions. Models with intractable normalizing functions arise in a wide variety of areas, for instance network models, models for…
Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…
The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…
In this work, we consider robust submodular maximization with matroid constraints. We give an efficient bi-criteria approximation algorithm that outputs a small family of feasible sets whose union has (nearly) optimal objective value. This…
A fast algorithm for the approximate multiplication of matrices with decay is introduced; the Sparse Approximate Matrix Multiply (SpAMM) reduces complexity in the product space, a different approach from current methods that economize…
With a high probability the Sarlos randomized algorithm of 2006 outputs a nearly optimal least squares solution of a highly overdeterminedlinear system of equations. We propose its simple deterministic variation which computes such a…
We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…