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What You Can Do with Coordinated Samples

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2013, RANDOM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8096))

Abstract

Sample coordination, where similar instances have similar samples, was proposed by statisticians four decades ago as a way to maximize overlap in repeated surveys. Coordinated sampling had been since used for summarizing massive data sets.

The usefulness of a sampling scheme hinges on the scope and accuracy within which queries posed over the original data can be answered from the sample. We aim here to gain a fundamental understanding of the limits and potential of coordination. Our main result is a precise characterization, in terms of simple properties of the estimated function, of queries for which estimators with desirable properties exist. We consider unbiasedness, nonnegativity, finite variance, and bounded estimates.

Since generally a single estimator can not be optimal (minimize variance simultaneously) for all data, we propose variance competitiveness, which means that the expectation of the square on any data is not too far from the minimum one possible for the data. Surprisingly perhaps, we show how to construct, for any function for which an unbiased nonnegative estimator exists, a variance competitive estimator.

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Author information

Authors and Affiliations

  1. Microsoft Research, SVC, USA

    Edith Cohen

  2. The Blavatnik School of Computer Science, Tel Aviv University, Israel

    Edith Cohen & Haim Kaplan

Authors
  1. Edith Cohen
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  2. Haim Kaplan
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Editors and Affiliations

  1. University of California, Berkeley, CA, USA

    Prasad Raghavendra

  2. Dept. of computer Science and Engineering, Pennsylvania State University, University Park, PA, USA

    Sofya Raskhodnikova

  3. Institute of Computer Science, University of Kiel, 24118, Kiel, Germany

    Klaus Jansen

  4. University of Geneva, Centre Universitaire d’Informatique, 1227, Carouge, Switzerland

    José D. P. Rolim

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Cohen, E., Kaplan, H. (2013). What You Can Do with Coordinated Samples. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2013 2013. Lecture Notes in Computer Science, vol 8096. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40328-6_32

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  • DOI: https://doi.org/10.1007/978-3-642-40328-6_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40327-9

  • Online ISBN: 978-3-642-40328-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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