Universal probability-free prediction

TL;DR

This paper introduces universal, assumption-free prediction systems inspired by falsifiability and Kolmogorov complexity, establishing a new theory of algorithmic randomness for time series.

Contribution

It develops universal prediction systems that do not rely on statistical assumptions and connects them with a novel theory of algorithmic complexity and randomness in time.

Findings

Prediction systems dominate conformal prediction under IID assumptions

New notions of algorithmic complexity for time series are introduced

Theoretical framework unifies falsifiability, Kolmogorov complexity, and randomness

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.