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Algorithmic Statistics and Prediction for Polynomial Time-Bounded Algorithms

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Sailing Routes in the World of Computation (CiE 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10936))

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Abstract

Algorithmic statistics studies explanations of observed data that are good in the algorithmic sense: an explanation should be simple i.e. should have small Kolmogorov complexity and capture all the algorithmically discoverable regularities in the data. However this idea can not be used in practice as is because Kolmogorov complexity is not computable.

In recent years resource-bounded algorithmic statistics were created [7, 8]. In this paper we prove a polynomial-time version of the following result of ‘classic’ algorithmic statistics.

Assume that some data were obtained as a result of some unknown experiment. What kind of data should we expect in similar situation (repeating the same experiment)? It turns out that the answer to this question can be formulated in terms of algorithmic statistics [6]. We prove a polynomial-time version of this result under a reasonable complexity theoretic assumption. The same assumption was used by Antunes and Fortnow [1].

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References

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Acknowledgments

This work is supported in parts by the RFBR grant 16-01-00362, by the Young Russian Mathematics award, MK-5379.2018.1 and the RaCAF ANR-15-CE40-0016-01 grant. The study has also been funded by the Russian Academic Excellence Project ‘5-100’.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow Institute of Physics and Technology, Moscow, Russia

    Alexey Milovanov

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  1. Alexey Milovanov
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Correspondence to Alexey Milovanov .

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Editors and Affiliations

  1. Kiel University, Kiel, Germany

    Florin Manea

  2. Queens College, CUNY, Queens, New York, USA

    Russell G. Miller

  3. Kiel University, Kiel, Germany

    Dirk Nowotka

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Milovanov, A. (2018). Algorithmic Statistics and Prediction for Polynomial Time-Bounded Algorithms. In: Manea, F., Miller, R., Nowotka, D. (eds) Sailing Routes in the World of Computation. CiE 2018. Lecture Notes in Computer Science(), vol 10936. Springer, Cham. https://doi.org/10.1007/978-3-319-94418-0_29

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  • DOI: https://doi.org/10.1007/978-3-319-94418-0_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94417-3

  • Online ISBN: 978-3-319-94418-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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