Algorithmic identification of probabilities is hard

Autores
Bienvenu, Laurent; Figueira, Santiago; Monin, Benoit; Shen, Alexander
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Reading more and more bits from an infinite binary sequence that is random for a Bernoulli measure with parameter p, we can get better and better approximations of p using the strong law of large numbers. In this paper, we study a similar situation from the viewpoint of inductive inference. Assume that p is a computable real, and we have to eventually guess the program that computes p. We show that this cannot be done computably, and extend this result to more general computable distributions. We also provide a weak positive result showing that looking at a sequence X generated according to some computable probability measure, we can guess a sequence of algorithms that, starting from some point, compute a measure that makes X Martin-Löf random.
Fil: Bienvenu, Laurent. Centre National de la Recherche Scientifique; Francia
Fil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; Argentina
Fil: Monin, Benoit. Université Paris-Est Créteil; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Shen, Alexander. Centre National de la Recherche Scientifique; Francia
Materia
ALGORITHMIC LEARNING THEORY
ALGORITHMIC RANDOMNESS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/98229
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Algorithmic identification of probabilities is hardBienvenu, LaurentFigueira, SantiagoMonin, BenoitShen, AlexanderALGORITHMIC LEARNING THEORYALGORITHMIC RANDOMNESShttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1Reading more and more bits from an infinite binary sequence that is random for a Bernoulli measure with parameter p, we can get better and better approximations of p using the strong law of large numbers. In this paper, we study a similar situation from the viewpoint of inductive inference. Assume that p is a computable real, and we have to eventually guess the program that computes p. We show that this cannot be done computably, and extend this result to more general computable distributions. We also provide a weak positive result showing that looking at a sequence X generated according to some computable probability measure, we can guess a sequence of algorithms that, starting from some point, compute a measure that makes X Martin-Löf random.Fil: Bienvenu, Laurent. Centre National de la Recherche Scientifique; FranciaFil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; ArgentinaFil: Monin, Benoit. Université Paris-Est Créteil; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Shen, Alexander. Centre National de la Recherche Scientifique; FranciaAcademic Press Inc Elsevier Science2018-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/98229Bienvenu, Laurent; Figueira, Santiago; Monin, Benoit; Shen, Alexander; Algorithmic identification of probabilities is hard; Academic Press Inc Elsevier Science; Journal of Computer and System Sciences; 95; 8-2018; 98-1080022-0000CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022000018301193info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jcss.2018.01.002info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:49:35Zoai:ri.conicet.gov.ar:11336/98229instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:49:36.045CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Algorithmic identification of probabilities is hard
title Algorithmic identification of probabilities is hard
spellingShingle Algorithmic identification of probabilities is hard
Bienvenu, Laurent
ALGORITHMIC LEARNING THEORY
ALGORITHMIC RANDOMNESS
title_short Algorithmic identification of probabilities is hard
title_full Algorithmic identification of probabilities is hard
title_fullStr Algorithmic identification of probabilities is hard
title_full_unstemmed Algorithmic identification of probabilities is hard
title_sort Algorithmic identification of probabilities is hard
dc.creator.none.fl_str_mv Bienvenu, Laurent
Figueira, Santiago
Monin, Benoit
Shen, Alexander
author Bienvenu, Laurent
author_facet Bienvenu, Laurent
Figueira, Santiago
Monin, Benoit
Shen, Alexander
author_role author
author2 Figueira, Santiago
Monin, Benoit
Shen, Alexander
author2_role author
author
author
dc.subject.none.fl_str_mv ALGORITHMIC LEARNING THEORY
ALGORITHMIC RANDOMNESS
topic ALGORITHMIC LEARNING THEORY
ALGORITHMIC RANDOMNESS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Reading more and more bits from an infinite binary sequence that is random for a Bernoulli measure with parameter p, we can get better and better approximations of p using the strong law of large numbers. In this paper, we study a similar situation from the viewpoint of inductive inference. Assume that p is a computable real, and we have to eventually guess the program that computes p. We show that this cannot be done computably, and extend this result to more general computable distributions. We also provide a weak positive result showing that looking at a sequence X generated according to some computable probability measure, we can guess a sequence of algorithms that, starting from some point, compute a measure that makes X Martin-Löf random.
Fil: Bienvenu, Laurent. Centre National de la Recherche Scientifique; Francia
Fil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación En Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación En Ciencias de la Computacion; Argentina
Fil: Monin, Benoit. Université Paris-Est Créteil; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Shen, Alexander. Centre National de la Recherche Scientifique; Francia
description Reading more and more bits from an infinite binary sequence that is random for a Bernoulli measure with parameter p, we can get better and better approximations of p using the strong law of large numbers. In this paper, we study a similar situation from the viewpoint of inductive inference. Assume that p is a computable real, and we have to eventually guess the program that computes p. We show that this cannot be done computably, and extend this result to more general computable distributions. We also provide a weak positive result showing that looking at a sequence X generated according to some computable probability measure, we can guess a sequence of algorithms that, starting from some point, compute a measure that makes X Martin-Löf random.
publishDate 2018
dc.date.none.fl_str_mv 2018-08
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/98229
Bienvenu, Laurent; Figueira, Santiago; Monin, Benoit; Shen, Alexander; Algorithmic identification of probabilities is hard; Academic Press Inc Elsevier Science; Journal of Computer and System Sciences; 95; 8-2018; 98-108
0022-0000
CONICET Digital
CONICET
url http://hdl.handle.net/11336/98229
identifier_str_mv Bienvenu, Laurent; Figueira, Santiago; Monin, Benoit; Shen, Alexander; Algorithmic identification of probabilities is hard; Academic Press Inc Elsevier Science; Journal of Computer and System Sciences; 95; 8-2018; 98-108
0022-0000
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022000018301193
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jcss.2018.01.002
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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