Universal Relationships in Measures of Unpredictability

TL;DR

This paper explores universal properties of sequence unpredictability, showing that certain relationships between sequences hold across all predictor classes satisfying specific axioms, revealing fundamental predictability limits.

Contribution

It establishes universal relationships in unpredictability measures that are independent of the predictor class, under certain axioms, advancing theoretical understanding.

Findings

Universal relationships between sequences' unpredictability are demonstrated.

These relationships hold for any predictor class satisfying the axioms.

The work reveals fundamental limits of sequence predictability.

Abstract

The predictability of a sequence is defined as the asymptotic performance of the best performing predictor in a given class. The value of the predictability of a sequence will in general depend on the choice of this predictor class. The existence of universal properties of predictability is demonstrated by looking at relationships between different sequences - these relationships hold for any class of predictors satisfying a certain set of axioms.