The massive volume of data generated in modern applications can overwhelm our ability to conveniently transmit, store, and index it. For many scenarios, building a compact summary of a dataset that is vastly smaller enables flexibility and efficiency in a range of queries over the data, in exchange for some approximation. This comprehensive introduction to data summarization, aimed at practitioners and students, showcases the algorithms, their behavior, and the mathematical underpinnings of their operation. The coverage starts with simple sums and approximate counts, building to more advanced probabilistic structures such as the Bloom Filter, distinct value summaries, sketches, and quantile summaries. Summaries are described for specific types of data, such as geometric data, graphs, and vectors and matrices. The authors offer detailed descriptions of and pseudocode for key algorithms that have been incorporated in systems from companies such as Google, Apple, Microsoft, Netflix and Twitter.

Small Summaries for Big Data

Computers & Technology

Cormode, Graham

Yi, Ke

Databases & Big Data

Cambridge University Press

Synopses for Massive Data: Samples, Histograms, Wavelets, Sketches describes basic principles and recent developments in building approximate synopses (i.e., lossy, compressed representations) of massive data. Such synopses enable approximate query processing, in which the user's query is executed against the synopsis instead of the original data. The monograph focuses on the four main families of synopses: random samples, histograms, wavelets, and sketches. A random sample comprises a "representative" subset of the data values of interest, obtained via a stochastic mechanism. Samples can be quick to obtain, and can be used to approximately answer a wide range of queries. A histogram summarizes a data set by grouping the data values into subsets, or "buckets," and then, for each bucket, computing a small set of summary statistics that can be used to approximately reconstruct the data in the bucket. Histograms have been extensively studied and have been incorporated into the query optimizers of virtually all commercial relational DBMSs. Wavelet-based synopses were originally developed in the context of image and signal processing. The data set is viewed as a set of M elements in a vector - i.e., as a function defined on the set {0, 1, 2, . . . , M-1} - and the wavelet transform of this function is found as a weighted sum of wavelet "basis functions." The weights, or coefficients, can then be "thresholded", for example, by eliminating coefficients that are close to zero in magnitude. The remaining small set of coefficients serves as the synopsis. Wavelets are good at capturing features of the data set at various scales. Sketch summaries are particularly well suited to streaming data. Linear sketches, for example, view a numerical data set as a vector or matrix, and multiply the data by a fixed matrix. Such sketches are massively parallelizable. They can accommodate streams of transactions in which data is both inserted and removed. Sketches have also been used successfully to estimate the answer to COUNT DISTINCT queries, a notoriously hard problem. Synopses for Massive Data describes and compares the different synopsis methods. It also discusses the use of AQP within research systems, and discusses challenges and future directions. It is essential reading for anyone working with, or doing research on massive data.

Synopses for Massive Data: Samples, Histograms, Wavelets, Sketches (Foundations and Trends(r) in Databases)

Haas, Peter J.

Garofalakis, Minos

Jermaine, Chris

Computer Science

Now Publishers

The term Federated Learning was coined as recently as 2016 to describe a machine learning setting where multiple entities collaborate in solving a machine learning problem, under the coordination of a central server or service provider. Each client's raw data is stored locally and not exchanged or transferred; instead, focused updates intended for immediate aggregation are used to achieve the learning objective.Since then, the topic has gathered much interest across many different disciplines and the realization that solving many of these interdisciplinary problems likely requires not just machine learning but techniques from distributed optimization, cryptography, security, differential privacy, fairness, compressed sensing, systems, information theory, statistics, and more.This monograph has contributions from leading experts across the disciplines, who describe the latest state-of-the art from their perspective. These contributions have been carefully curated into a comprehensive treatment that enables the reader to understand the work that has been done and get pointers to where effort is required to solve many of the problems before Federated Learning can become a reality in practical systems.Researchers working in the area of distributed systems will find this monograph an enlightening read that may inspire them to work on the many challenging issues that are outlined. This monograph will get the reader up to speed quickly and easily on what is likely to become an increasingly important topic: Federated Learning.

Advances and Open Problems in Federated Learning (Foundations and Trends(r) in Machine Learning)

Hutchinson, Ben

Raskar, Ramesh

Mohri, Mehryar

Liu, Yang

Yang, Qiang

Yu, Han

Bennis, Mehdi

Evans,David

Song, Dawn

Joshi, Gauri

Kairouz, Peter

McMahan, H Brendan

Avent, Brendan

Bellet, Aurélien

Bhagoji, Arjun Nitin

Bonawit, Kallista

Charles, Zachary

Cummings, Rachel

D'Oliveira, Rafael G L

Eichner, Hubert

El Rouayheb, Salim

Gardner, Josh

Garrett, Zachary

Gascón, Adrià

Ghazi, Badih

Gibbons, Phillip B

Gruteser, Marco

Harchaoui, Zaid

He, Chaoyang

He, Lie

Huo, Zhouyuan

Hsu, Justin

Jäggi, Martin

Javidi, Tara

Khodak, Mikhail

Konecný, Jakub

Korolova, Aleksandra

Koushanfar, Farinaz

Koyejo, Sanmi

Lepoint, Tancrède

Mittal, Prateek

Nock, Richard

Özgür, Ayfer

Pagh, Rasmus

Qi, Hang

Ramage, Daniel

Raykova, Mariana

Song, Weikang

Stich, Sebastian U

Sun, Ziteng

Theertha Suresh, Ananda

Tramèr, Florian

Vepakomma, Praneeth

Wang, Jianyu

Xiong, Li

Xu, Zheng

Yu, Felix X

Zhao, Sen

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