Universal probability-free prediction
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.
KeywordsConformal 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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