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In environmental studies, realistic simulations are essential for understanding complex systems. Statistical emulation with Gaussian processes (GPs) in functional data models have become a standard tool for this purpose. Traditional…

Applications · Statistics 2024-09-26 R. Jacob Andros , Rajarshi Guhaniyogi , Devin Francom , Donatella Pasqualini

This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…

Statistics Theory · Mathematics 2018-08-29 Stanislav Minsker , Nate Strawn

Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. We propose a "compressive learning" framework where we estimate model parameters from a sketch of the training data. This sketch…

Machine Learning · Computer Science 2017-05-08 Nicolas Keriven , Anthony Bourrier , Rémi Gribonval , Patrick Pérez

We propose a novel Bayesian inference framework for distributed differentially private linear regression. We consider a distributed setting where multiple parties hold parts of the data and share certain summary statistics of their portions…

Machine Learning · Statistics 2023-06-08 Barış Alparslan , Sinan Yıldırım , Ş. İlker Birbil

In this work, we propose a novel framework for privacy-preserving client-distributed machine learning. It is motivated by the desire to achieve differential privacy guarantees in the local model of privacy in a way that satisfies all…

Cryptography and Security · Computer Science 2018-10-12 Vasyl Pihur , Aleksandra Korolova , Frederick Liu , Subhash Sankuratripati , Moti Yung , Dachuan Huang , Ruogu Zeng

We study the privatization of distributed learning and optimization strategies. We focus on differential privacy schemes and study their effect on performance. We show that the popular additive random perturbation scheme degrades…

Machine Learning · Computer Science 2023-01-18 Elsa Rizk , Stefan Vlaski , Ali H. Sayed

In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…

Optimization and Control · Mathematics 2018-08-09 Ion Necoara , Martin Takac

This survey highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compresses it to a much smaller matrix by multiplying it by a…

Data Structures and Algorithms · Computer Science 2015-02-11 David P. Woodruff

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…

Databases · Computer Science 2015-03-20 Odysseas Papapetrou , Minos Garofalakis , Antonios Deligiannakis

Linear regression is a classic method of data analysis. In recent years, sketching -- a method of dimension reduction using random sampling, random projections, or both -- has gained popularity as an effective computational approximation…

Machine Learning · Statistics 2020-08-04 Jocelyn T. Chi , Ilse C. F. Ipsen

Sketch-and-project is a framework which unifies many known iterative methods for solving linear systems and their variants, as well as further extensions to non-linear optimization problems. It includes popular methods such as randomized…

Optimization and Control · Mathematics 2023-09-20 Michał Dereziński , Elizaveta Rebrova

Distributed machine learning has been widely studied in order to handle exploding amount of data. In this paper, we study an important yet less visited distributed learning problem where features are inherently distributed or vertically…

Machine Learning · Computer Science 2019-07-19 Yaochen Hu , Peng Liu , Linglong Kong , Di Niu

Linear sketches have been widely adopted to process fast data streams, and they can be used to accurately answer frequency estimation, approximate top K items, and summarize data distributions. When data are sensitive, it is desirable to…

Data Structures and Algorithms · Computer Science 2022-10-18 Fuheng Zhao , Dan Qiao , Rachel Redberg , Divyakant Agrawal , Amr El Abbadi , Yu-Xiang Wang

Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number…

Optimization and Control · Mathematics 2019-06-03 Albert S. Berahas , Raghu Bollapragada , Jorge Nocedal

This paper presents a holistic approach to gradient leakage resilient distributed Stochastic Gradient Descent (SGD). First, we analyze two types of strategies for privacy-enhanced federated learning: (i) gradient pruning with random…

Machine Learning · Computer Science 2023-05-12 Wenqi Wei , Ling Liu , Jingya Zhou , Ka-Ho Chow , Yanzhao Wu

A continuing challenge for machine learning is providing methods to perform computation on data while ensuring the data remains private. In this paper we build on the provable privacy guarantees of differential privacy which has been…

Machine Learning · Computer Science 2019-09-23 Michael Thomas Smith , Mauricio A. Alvarez , Neil D. Lawrence

As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine…

Machine Learning · Statistics 2019-12-10 Biyi Fang , Diego Klabjan

Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…

Numerical Analysis · Mathematics 2020-12-23 Vivak Patel , Mohammad Jahangoshahi , Daniel Adrian Maldonado

Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck.…

Statistics Theory · Mathematics 2022-10-25 Edgar Dobriban , Yue Sheng

The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data.…

Machine Learning · Statistics 2018-02-08 Panagiotis A. Traganitis , Georgios B. Giannakis