Abstract
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.
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Acknowledgements
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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This work has been supported by the Air Force Office of Scientific Research (grant “Semantic Completions”), EPSRC (grant EP/K033344/1), and the EU Horizon 2020 Research and Innovation programme (grant 671555).
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Vovk, V., Pavlovic, D. Universal probability-free prediction. Ann Math Artif Intell 81, 47–70 (2017). https://doi.org/10.1007/s10472-017-9547-9
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DOI: https://doi.org/10.1007/s10472-017-9547-9