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Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in…

Methodology · Statistics 2020-08-14 Toshihiro Hirano

We consider the problem of estimating the trace of a matrix function $f(A)$. In certain situations, in particular if $f(A)$ cannot be well approximated by a low-rank matrix, combining probing methods based on graph colorings with stochastic…

Numerical Analysis · Mathematics 2023-08-16 Andreas Frommer , Michele Rinelli , Marcel Schweitzer

Randomized subspace approximation with "matrix sketching" is an effective approach for constructing approximate partial singular value decompositions (SVDs) of large matrices. The performance of such techniques has been extensively…

Numerical Analysis · Mathematics 2024-06-28 Yijun Dong , Per-Gunnar Martinsson , Yuji Nakatsukasa

We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform…

Machine Learning · Computer Science 2020-10-26 Jonathan Lacotte , Mert Pilanci

We focus the use of \emph{row sampling} for approximating matrix algorithms. We give applications to matrix multipication; sparse matrix reconstruction; and, \math{\ell_2} regression. For a matrix \math{\matA\in\R^{m\times d}} which…

Data Structures and Algorithms · Computer Science 2010-08-04 Malik Magdon-Ismail

The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling. The approximation problem in Frobenius norm admits a well-known…

Optimization and Control · Mathematics 2023-12-08 Mareike Dressler , André Uschmajew , Venkat Chandrasekaran

Stream monitoring is fundamental in many data stream applications, such as financial data trackers, security, anomaly detection, and load balancing. In that respect, quantiles are of particular interest, as they often capture the user's…

Data Structures and Algorithms · Computer Science 2022-01-07 Rana Shahout , Roy Friedman , Ran Ben Basat

Large-scale distributed training of neural networks is often limited by network bandwidth, wherein the communication time overwhelms the local computation time. Motivated by the success of sketching methods in sub-linear/streaming…

Machine Learning · Computer Science 2020-01-24 Nikita Ivkin , Daniel Rothchild , Enayat Ullah , Vladimir Braverman , Ion Stoica , Raman Arora

Counting small subgraphs, referred to as motifs, in large graphs is a fundamental task in graph analysis, extensively studied across various contexts and computational models. In the sublinear-time regime, the relaxed problem of approximate…

Data Structures and Algorithms · Computer Science 2025-03-14 Talya Eden , Reut Levi , Dana Ron , Ronitt Rubinfeld

Varying coefficient models are popular for estimating nonlinear regression functions in functional data models. Their Bayesian variants have received limited attention in large data applications, primarily due to prohibitively slow…

Machine Learning · Statistics 2025-06-03 Rajarshi Guhaniyogi , Laura Baracaldo , Sudipto Banerjee

Given a symmetric matrix $A$, we show from the simple sketch $GAG^T$, where $G$ is a Gaussian matrix with $k = O(1/\epsilon^2)$ rows, that there is a procedure for approximating all eigenvalues of $A$ simultaneously to within $\epsilon…

Data Structures and Algorithms · Computer Science 2023-04-20 William Swartworth , David P. Woodruff

As sketch research has collectively matured over time, its adaptation for at-mass commercialisation emerges on the immediate horizon. Despite an already mature research endeavour for photos, there is no research on the efficient inference…

Computer Vision and Pattern Recognition · Computer Science 2025-05-30 Aneeshan Sain , Subhajit Maity , Pinaki Nath Chowdhury , Subhadeep Koley , Ayan Kumar Bhunia , Yi-Zhe Song

To see is to sketch -- free-hand sketching naturally builds ties between human and machine vision. In this paper, we present a novel approach for translating an object photo to a sketch, mimicking the human sketching process. This is an…

Computer Vision and Pattern Recognition · Computer Science 2018-05-02 Jifei Song , Kaiyue Pang , Yi-Zhe Song , Tao Xiang , Timothy Hospedales

The Count-Min Sketch is a widely adopted structure for approximate event counting in large scale processing. In a previous work we improved the original version of the Count-Min-Sketch (CMS) with conservative update using approximate…

Information Retrieval · Computer Science 2016-06-16 Guillaume Pitel , Geoffroy Fouquier , Emmanuel Marchand , Abdul Mouhamadsultane

Learning-based low rank approximation algorithms can significantly improve the performance of randomized low rank approximation with sketch matrix. With the learned value and fixed non-zero positions for sketch matrices from learning-based…

Machine Learning · Computer Science 2022-12-19 Tiejin Chen , Yicheng Tao

We generalize the leverage score sampling sketch for $\ell_2$-subspace embeddings, to accommodate sampling subsets of the transformed data, so that the sketching approach is appropriate for distributed settings. This is then used to derive…

Information Theory · Computer Science 2024-06-27 Neophytos Charalambides , Mert Pilanci , Alfred Hero

Data sketches are approximate succinct summaries of long streams. They are widely used for processing massive amounts of data and answering statistical queries about it in real-time. Existing libraries producing sketches are very fast, but…

Data Structures and Algorithms · Computer Science 2019-12-06 Arik Rinberg , Alexander Spiegelman , Edward Bortnikov , Eshcar Hillel , Idit Keidar , Lee Rhodes , Hadar Serviansky

Sketch-based streaming algorithms allow efficient processing of big data. These algorithms use small fixed-size storage to store a summary ("sketch") of the input data, and use probabilistic algorithms to estimate the desired quantity.…

Databases · Computer Science 2016-11-08 Reuven Cohen , Liran Katzir , Aviv Yehezkel

Identifying independence between two random variables or correlated given their samples has been a fundamental problem in Statistics. However, how to do so in a space-efficient way if the number of states is large is not quite well-studied.…

Data Structures and Algorithms · Computer Science 2022-11-21 Zhenhao Gu , Hao Zhang

Many recent prompting strategies for large language models (LLMs) query the model multiple times sequentially -- first to produce intermediate results and then the final answer. However, using these methods, both decoder and model are…

Computation and Language · Computer Science 2023-11-10 Luca Beurer-Kellner , Mark Niklas Müller , Marc Fischer , Martin Vechev