Universal probability-free prediction

  • Vladimir Vovk
  • Dusko Pavlovic
Open Access


We construct universal prediction systems in the spirit of Popper’s falsifiability and Kolmogorov complexity and randomness. These prediction systems do not depend on any statistical assumptions (but under the IID assumption they dominate, to within the usual accuracy, conformal prediction). Our constructions give rise to a theory of algorithmic complexity and randomness of time containing analogues of several notions and results of the classical theory of Kolmogorov complexity and randomness.


Conformal prediction Prediction systems Probability-free learning Universal prediction 

Mathematics Subject Classification (2010)

68Q30 60G25 62M20 68Q32 68T05 62G15 



We thank the anonymous referees of the conference and journal versions of this paper for helpful comments. In particular, comments made by the referees of the journal version have led to Remarks 2 and 7, and we especially appreciate their generosity in filling a gap in the proof of Theorem 18.


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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Royal Holloway, University of LondonEghamUK
  2. 2.University of HawaiiHonoluluUSA

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