Streaming Algorithms from Precision Sampling
Alexandr Andoni, Robert Krauthgamer, Krzysztof Onak

TL;DR
This paper introduces a unified probabilistic method called Precision Sampling to develop simple, efficient streaming algorithms for estimating various norms and moments of data streams, improving upon previous techniques.
Contribution
It demonstrates that multiple recent data-stream algorithms can be derived from a single Precision Sampling approach, simplifying the design and analysis of these algorithms.
Findings
Unified framework for streaming algorithms using Precision Sampling
Efficient estimation of $F_k$-moments and $\, ext{l}_p$-norms
Linear sketching allows for general updates and broad applicability
Abstract
A technique introduced by Indyk and Woodruff [STOC 2005] has inspired several recent advances in data-stream algorithms. We show that a number of these results follow easily from the application of a single probabilistic method called Precision Sampling. Using this method, we obtain simple data-stream algorithms that maintain a randomized sketch of an input vector , which is useful for the following applications. 1) Estimating the -moment of , for . 2) Estimating the -norm of , for , with small update time. 3) Estimating cascaded norms for all . 4) sampling, where the goal is to produce an element with probability (approximately) . It extends to similarly defined -sampling, for . For all these applications the algorithm is essentially the same: scale the vector x…
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Taxonomy
TopicsMachine Learning and Algorithms · Algorithms and Data Compression · Data Stream Mining Techniques
