Related papers: Optimal Matrix Sketching over Sliding Windows
Determinant maximization problem gives a general framework that models problems arising in as diverse fields as statistics \cite{pukelsheim2006optimal}, convex geometry \cite{Khachiyan1996}, fair allocations\linebreak \cite{anari2016nash},…
In this work we propose a new paradigm for designing efficient deep unrolling networks using operator sketching. The deep unrolling networks are currently the state-of-the-art solutions for imaging inverse problems. However, for…
We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of $n\times n$ matrices and an $n$-dimensional vector, find a sequence of $K$ matrices, each chosen from the…
We consider the classical Minimum Crossing Number problem: given an $n$-vertex graph $G$, compute a drawing of $G$ in the plane, while minimizing the number of crossings between the images of its edges. This is a fundamental and extensively…
Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…
We improve upon previous oblivious sketching and turnstile streaming results for $\ell_1$ and logistic regression, giving a much smaller sketching dimension achieving $O(1)$-approximation and yielding an efficient optimization problem in…
We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error. Importantly, this…
This paper resolves one of the longest standing basic problems in the streaming computational model. Namely, optimal construction of quantile sketches. An $\varepsilon$ approximate quantile sketch receives a stream of items $x_1,\ldots,x_n$…
In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension…
Power iteration can improve the accuracy of randomized SVD, but requires multiple data passes, making it impractical in streaming or memory-constrained settings. We introduce a lightweight yet effective sketch-power iteration, allowing…
We investigate iterative methods with randomized preconditioners for solving overdetermined least-squares problems, where the preconditioners are based on a random embedding of the data matrix. We consider two distinct approaches: the…
The matrix scaling problem, particularly the Sinkhorn-Knopp algorithm, has been studied for over 60 years. In practice, the algorithm often yields high-quality approximations within just a few iterations. Theoretically, however, the…
When machine learning models are trained continually on a sequence of tasks, they are often liable to forget what they learned on previous tasks--a phenomenon known as catastrophic forgetting. Proposed solutions to catastrophic forgetting…
In second-order optimization, a potential bottleneck can be computing the Hessian matrix of the optimized function at every iteration. Randomized sketching has emerged as a powerful technique for constructing estimates of the Hessian which…
The metric sketching problem is defined as follows. Given a metric on $n$ points, and $\epsilon>0$, we wish to produce a small size data structure (sketch) that, given any pair of point indices, recovers the distance between the points up…
In this note, we develop fast and deterministic dimensionality reduction techniques for a family of subspace approximation problems. Let $P\subset \mathbbm{R}^N$ be a given set of $M$ points. The techniques developed herein find an $O(n…
Randomized algorithms are important for solving large-scale optimization problems. In this paper, we propose a fast sketching algorithm for least square problems regularized by convex or nonconvex regularization functions, Sketching for…
Detecting maximal square submatrices of ones in binary matrices is a fundamental problem with applications in computer vision and pattern recognition. While the standard dynamic programming (DP) solution achieves optimal asymptotic…
While traditional data-management systems focus on evaluating single, ad-hoc queries over static data sets in a centralized setting, several emerging applications require (possibly, continuous) answers to queries on dynamic data that is…
The sliding window model generalizes the standard streaming model and often performs better in applications where recent data is more important or more accurate than data that arrived prior to a certain time. We study the problem of…