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Computable Exchangeable Sequences Have Computable de Finetti Measures

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Mathematical Theory and Computational Practice (CiE 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5635))

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Abstract

We prove a uniformly computable version of de Finetti’s theorem on exchangeable sequences of real random variables. In the process, we develop machinery for computably recovering a distribution from its sequence of moments, which suffices to prove the theorem in the case of (almost surely) continuous directing random measures. In the general case, we give a proof inspired by a randomized algorithm which succeeds with probability one. Finally, we show how, as a consequence of the main theorem, exchangeable stochastic processes in probabilistic functional programming languages can be rewritten as procedures that do not use mutation.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, USA

    Cameron E. Freer

  2. Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, USA

    Daniel M. Roy

Authors
  1. Cameron E. Freer
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  2. Daniel M. Roy
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Editor information

Editors and Affiliations

  1. University of Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    Klaus Ambos-Spies

  2. Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, Amsterdam, TV, The Netherlands

    Benedikt Löwe

  3. Institut für Informatik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    Wolfgang Merkle

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Freer, C.E., Roy, D.M. (2009). Computable Exchangeable Sequences Have Computable de Finetti Measures. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds) Mathematical Theory and Computational Practice. CiE 2009. Lecture Notes in Computer Science, vol 5635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03073-4_23

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  • DOI: https://doi.org/10.1007/978-3-642-03073-4_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03072-7

  • Online ISBN: 978-3-642-03073-4

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