A Generalized Characterization of Algorithmic Probability

Tom F. Sterkenburg

doi:10.1007/s00224-017-9774-9

A Generalized Characterization of Algorithmic Probability

Tom F. Sterkenburg^*

^*Corresponding author for this work

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3 Citations (Scopus)

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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 association of algorithmic probability with certain foundational principles of statistics.

Original language	English
Pages (from-to)	1337-1352
Number of pages	16
Journal	Theory of computing systems
Volume	61
Issue number	4
DOIs	https://doi.org/10.1007/s00224-017-9774-9
Publication status	Published - Nov-2017
Event	10th International Conference on Computability, Complexity and Randomness (CCR) - Heidelberg, Germany Duration: 22-Jun-2015 → 26-Jun-2015

Keywords

Algorithmic probability
A priori semimeasure
Semicomputable semimeasures
Monotone turing machines
Principle of indifference
Occam's razor
INDUCTION

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title = "A Generalized Characterization of Algorithmic Probability",

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 association of algorithmic probability with certain foundational principles of statistics.",

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language = "English",

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journal = "Theory of computing systems",

issn = "1432-4350",

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T1 - A Generalized Characterization of Algorithmic Probability

AU - Sterkenburg, Tom F.

PY - 2017/11

Y1 - 2017/11

N2 - 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 association of algorithmic probability with certain foundational principles of statistics.

AB - 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 association of algorithmic probability with certain foundational principles of statistics.

KW - Algorithmic probability

KW - A priori semimeasure

KW - Semicomputable semimeasures

KW - Monotone turing machines

KW - Principle of indifference

KW - Occam's razor

KW - INDUCTION

U2 - 10.1007/s00224-017-9774-9

DO - 10.1007/s00224-017-9774-9

M3 - Article

SN - 1432-4350

VL - 61

SP - 1337

EP - 1352

JO - Theory of computing systems

JF - Theory of computing systems

IS - 4

T2 - 10th International Conference on Computability, Complexity and Randomness (CCR)

Y2 - 22 June 2015 through 26 June 2015

ER -

A Generalized Characterization of Algorithmic Probability

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Keywords

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