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Concentration Inequalities

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Advanced Lectures on Machine Learning (ML 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3176))

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Abstract

Concentration inequalities deal with deviations of functions of independent random variables from their expectation. In the last decade new tools have been introduced making it possible to establish simple and powerful inequalities. These inequalities are at the heart of the mathematical analysis of various problems in machine learning and made it possible to derive new efficient algorithms. This text attempts to summarize some of the basic tools.

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Author information

Authors and Affiliations

  1. Laboratoire d’Informatique, Université de Paris-Sud, Bâtiment 490, F-91405 Cedex, Orsay, France

    Stéphane Boucheron

  2. Department of Economics, Pompeu Fabra University, Ramon Trias Fargas 25-27, 08005, Barcelona, Spain

    Gábor Lugosi

  3. Max-Planck Institute for Biological Cybernetics, Spemannstr. 38, D-72076, Tübingen, Germany

    Olivier Bousquet

Authors
  1. Stéphane Boucheron
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  2. Gábor Lugosi
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  3. Olivier Bousquet
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Editor information

Editors and Affiliations

  1. Pertinence, 32 rue des Jeûneurs, 75002, Paris, France

    Olivier Bousquet

  2. Max Planck Institute for Biological Cybernetics, Spemannstr. 38, 72076, Tübingen, Germany

    Ulrike von Luxburg

  3. Friedrich Miescher Laboratory of the Max Planck Society, Spemannstr. 39, 72076, Tübingen, Germany

    Gunnar Rätsch

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Boucheron, S., Lugosi, G., Bousquet, O. (2004). Concentration Inequalities. In: Bousquet, O., von Luxburg, U., Rätsch, G. (eds) Advanced Lectures on Machine Learning. ML 2003. Lecture Notes in Computer Science(), vol 3176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28650-9_9

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  • DOI: https://doi.org/10.1007/978-3-540-28650-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23122-6

  • Online ISBN: 978-3-540-28650-9

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