Ann Math Artif Intell (2017) 81:47–70
Universal probability-free prediction
· Dusko Pavlovic
Published online: 19 April 2017
© The Author(s) 2017. This article is an open access publication
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 com-
plexity and randomness of time containing analogues of several notions and results of the
classical theory of Kolmogorov complexity and randomness.
Keywords Conformal prediction · Prediction systems · Probability-free learning ·
Mathematics Subject Classification (2010) 68Q30 · 60G25 · 62M20 · 68Q32 · 68T05 · 62G15
In this paper we consider the problem of predicting the labels, assumed to be binary, of a se-
quence of objects. This is an online version of the standard problem of binary classification.
Namely, we will be interested in infinite sequences of observations
ω = (z
),...) ∈ (X ×
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).
Royal Holloway, University of London, Egham, Surrey, UK
University of Hawaii, Honolulu, HI, USA