About: Solomonoff's theory of inductive inference

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Solomonoff's theory of inductive inference is a mathematical proof that if a universe is generated by an algorithm, then observations of that universe, encoded as a dataset, are best predicted by the smallest executable archive of that dataset. This formalization of Occam's razor for induction was introduced by Ray Solomonoff, based on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theory, given a sequence of observed data. This posterior probability is derived from Bayes rule and some universal prior, that is, a prior that assigns a positive probability to any computable theory.

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rdf:type	work
rdfs:label	نظرية سولومونوف في الاستدلال الاستقرائي (ar) Solomonoff's theory of inductive inference (en) Teoria da Inferência Indutiva de Solomonoff (pt) 所罗门诺夫的归纳推理理论 (zh)
rdfs:comment	نظرية سولومونوف في الاستدلال الاستقرائي هي دليل رياضي على أنه إذا تم إنشاء الكون من خلال خوارزمية، فمن الأفضل توقع ملاحظات هذا الكون كمجموعة بيانات، من خلال أصغر أرشيف قابل للتنفيذ لمجموعة البيانات هذه، تم تقديم هذا الشكل للحث بواسطة راي سولومونوف، بناءً على نظرية الاحتمالات وعلوم الحاسوب النظرية. يستمد استقراء سولومونوف اللاحتمال لأي نظرية قابلة للحساب، بالنظر إلى تسلسل البيانات المرصودة. يُشتق هذا الاحتمال اللاحق من قاعدة بايز وبعض القواعد العامة السابقة، أي السابقة التي تعين احتمالًا إيجابيًا لأي نظرية حسابية. (ar) Solomonoff's theory of inductive inference is a mathematical proof that if a universe is generated by an algorithm, then observations of that universe, encoded as a dataset, are best predicted by the smallest executable archive of that dataset. This formalization of Occam's razor for induction was introduced by Ray Solomonoff, based on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theory, given a sequence of observed data. This posterior probability is derived from Bayes rule and some universal prior, that is, a prior that assigns a positive probability to any computable theory. (en) A Teoria de Inferência Indutiva Universal de Solomonoff é uma teoria de predição baseada em observações lógicas, assim como predizendo o próximo símbolo baseada numa dada série de símbolos. A única suposição é de que o ambiente segue alguma distribuição probabilística desconhecida mas computável. Isso é uma lâmina de Occam matematicamente formalizada. (pt) 所罗门诺夫的归纳推理理论（Solomonoff's theory of inductive inference）是对奥卡姆剃刀叙述的数学化描述。该理论指出：在所有能够完全描述的已观测的可计算类中，较短的可计算理论在估计下一次观测结果的概率时具有较大的权重。简而言之，在几组可以给出的答案的假设论述中，假设越少的越被大家选择。引申为“越简单的越易行”。 (zh)
dcterms:subject	Algorithmic information theory Machine learning Inductive reasoning Statistical inference Bayesian statistics
Wikipage page ID	405562 (xsd:integer)
Wikipage revision ID	1080885244 (xsd:integer)
Link from a Wikipage to another Wikipage	Bayesian inference Bayesian probability Problem of induction Bayes' theorem Algorithm Algorithmic information theory Algorithmic probability Algorithmic information theory E. Mark Gold Inductive probability Computability Countable set Limit (math) MIT Press Stephen Kleene Computer science Machine learning Inductive reasoning Statistical inference William Gasarch Language identification in the limit Expected value No free lunch theorem Carl Herbert Smith Kolmogorov complexity Posterior probability Prior probability Probability Probability theory AIXI Bayesian statistics Bit array Ray Solomonoff Martin Davis (mathematician) Inductive reasoning Kullback–Leibler divergence Minimum description length Minimum message length Turing machine New riddle of induction Occam's razor Event loop Super-recursive algorithm Principle of Multiple Explanations Universal artificial intelligence Universal computer Mill's methods Inductive inference Computable dbr:Wikipedia:JARGON
Link from a Wikipage to an external page	http://world.std.com/~rjs/compj99.pdf http://www.cs.auckland.ac.nz/CDMTCS/researchreports/300nick.pdf http://www.scholarpedia.org/article/Algorithmic_probability https://dl.acm.org/doi/pdf/10.1145/356914.356918%7C http://world.std.com/~rjs/1964pt1.pdf http://world.std.com/~rjs/1964pt2.pdf
sameAs	Solomonoff's theory of inductive inference Solomonoff's theory of inductive inference Solomonoff's theory of inductive inference Solomonoff's theory of inductive inference Solomonoff's theory of inductive inference Solomonoff's theory of inductive inference
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has abstract	نظرية سولومونوف في الاستدلال الاستقرائي هي دليل رياضي على أنه إذا تم إنشاء الكون من خلال خوارزمية، فمن الأفضل توقع ملاحظات هذا الكون كمجموعة بيانات، من خلال أصغر أرشيف قابل للتنفيذ لمجموعة البيانات هذه، تم تقديم هذا الشكل للحث بواسطة راي سولومونوف، بناءً على نظرية الاحتمالات وعلوم الحاسوب النظرية. يستمد استقراء سولومونوف اللاحتمال لأي نظرية قابلة للحساب، بالنظر إلى تسلسل البيانات المرصودة. يُشتق هذا الاحتمال اللاحق من قاعدة بايز وبعض القواعد العامة السابقة، أي السابقة التي تعين احتمالًا إيجابيًا لأي نظرية حسابية. (ar) Solomonoff's theory of inductive inference is a mathematical proof that if a universe is generated by an algorithm, then observations of that universe, encoded as a dataset, are best predicted by the smallest executable archive of that dataset. This formalization of Occam's razor for induction was introduced by Ray Solomonoff, based on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theory, given a sequence of observed data. This posterior probability is derived from Bayes rule and some universal prior, that is, a prior that assigns a positive probability to any computable theory. (en) A Teoria de Inferência Indutiva Universal de Solomonoff é uma teoria de predição baseada em observações lógicas, assim como predizendo o próximo símbolo baseada numa dada série de símbolos. A única suposição é de que o ambiente segue alguma distribuição probabilística desconhecida mas computável. Isso é uma lâmina de Occam matematicamente formalizada. (pt) 所罗门诺夫的归纳推理理论（Solomonoff's theory of inductive inference）是对奥卡姆剃刀叙述的数学化描述。该理论指出：在所有能够完全描述的已观测的可计算类中，较短的可计算理论在估计下一次观测结果的概率时具有较大的权重。简而言之，在几组可以给出的答案的假设论述中，假设越少的越被大家选择。引申为“越简单的越易行”。 (zh)
gold:hypernym	Theory
prov:wasDerivedFrom	wikipedia-en:Solomonoff's_theory_of_inductive_inference?oldid=1080885244&ns=0
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foaf:isPrimaryTopicOf	wikipedia-en:Solomonoff's_theory_of_inductive_inference
is Link from a Wikipage to another Wikipage of	Bayesian inference Problem of induction Algorithmic information theory Algorithmic probability Anthropic principle Universality probability

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