A generalized characterization of algorithmic probability

TL;DR

This paper broadens the understanding of algorithmic probability by showing it can be characterized as transformations of any continuous computable measure, not just the uniform measure, using universal monotone Turing machines.

Contribution

It provides a generalized characterization of a priori semimeasures, extending the foundational framework of algorithmic probability beyond the uniform measure.

Findings

A priori semimeasures can be derived from any continuous computable measure.

Universal monotone Turing machines facilitate this transformation.

Implications for statistical principles in inductive inference are discussed.

Abstract

An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the infinite strings. It is shown in this paper that the class of a priori semimeasures can equivalently be defined as the class of transformations, by all compatible universal monotone Turing machines, of any continuous computable measure in place of the uniform measure. Some consideration is given to possible implications for the prevalent association of algorithmic probability with certain foundational statistical principles.