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- Algorithmic_probability abstract "In algorithmic information theory, algorithmic (Solomonoff) probability is a mathematical method of assigning a prior probability to a given observation. In a theoretic sense, the prior is universal. It is used in inductive inference theory, and analyses of algorithms. Since it is not computable, it must be approximated.It deals with the questions: Given a body of data about some phenomenon that one wants to understand, how can one select the most probable hypothesis of how it was caused from among all possible hypotheses, how can one evaluate the different hypotheses, and how can one predict future data? Algorithmic probability combines several ideas: Occam's razor; Epicurus' principle of multiple explanations; and special coding methods from modern computing theory. The prior obtained from the formula is used in Bayes rule for prediction.Occam's razor means 'among the theories that are consistent with the observed phenomena, one should select the simplest theory'.In contrast, Epicurus had proposed the Principle of Multiple Explanations: if more than one theory is consistent with the observations, keep all such theories.A special mathematical object called a universal Turing machine is used to compute, quantify and assign codes to all quantities of interest. The universal prior is taken over the class of all computable measures; no hypothesis will have a zero probability.Algorithmic probability combines Occam's razor and the principle of multiple explanations by giving a probability value to each hypothesis (algorithm or program) that explains a given observation, with the simplest hypothesis (the shortest program) having the highest probability and the increasingly complex hypotheses (longer programs) receiving increasingly small probabilities. These probabilities form a prior probability distribution for the observation, which Ray Solomonoff proved to be machine-invariant within a constant factor (called the invariance theorem) and can be used with Bayes' theorem to predict the most likely continuation of that observation. A universal Turing machine is used for the computer operations.Solomonoff invented the concept of algorithmic probability with its associated invariance theorem around 1960, publishing a report on it: "A Preliminary Report on a General Theory of Inductive Inference." He clarified these ideas more fully in 1964 with "A Formal Theory of Inductive Inference," Part I and Part II.He described a universal computer with a randomly generated input program. The program computes some possibly infinite output. The universal probability distribution is the probability distribution on all possible output strings with random input.The algorithmic probability of any given finite output prefix q is the sum of the probabilities of the programs that compute something starting with q. Certain long objects with short programs have high probability.Algorithmic probability is the main ingredient of Solomonoff's theory of inductive inference, the theory of prediction based on observations; it was invented with the goal of using it for machine learning; given a sequence of symbols, which one will come next? Solomonoff's theory provides an answer that is optimal in a certain sense, although it is incomputable. Unlike, for example, Karl Popper's informal inductive inference theory, Solomonoff's is mathematically rigorous. Algorithmic probability is closely related to the concept of Kolmogorov complexity. Kolmogorov's introduction of complexity, was motivated by information theory and problems in randomness while Solomonoff introduced algorithmic complexity for a different reason: inductive reasoning. A single universal prior probability that can be substituted for each actual prior probability in Bayes’s rule was invented by Solomonoff with Kolmogorov complexity as a side product.Solomonoff's enumerable measure is universal in a certain powerful sense, but the computation time can be infinite. One way of dealing with this is a variant of Leonid Levin's Search Algorithm, which limits the time spent computing the success of possible programs, with shorter programs given more time. Other methods of limiting the search space include training sequences.".
- Algorithmic_probability wikiPageExternalLink Algorithmic_probability.
- Algorithmic_probability wikiPageExternalLink pubs.html.
- Algorithmic_probability wikiPageID "402688".
- Algorithmic_probability wikiPageLength "7535".
- Algorithmic_probability wikiPageOutDegree "29".
- Algorithmic_probability wikiPageRevisionID "680371419".
- Algorithmic_probability wikiPageWikiLink Algorithmic_information_theory.
- Algorithmic_probability wikiPageWikiLink Andrey_Kolmogorov.
- Algorithmic_probability wikiPageWikiLink Bayes_theorem.
- Algorithmic_probability wikiPageWikiLink Bayesian_inference.
- Algorithmic_probability wikiPageWikiLink Category:Algorithmic_information_theory.
- Algorithmic_probability wikiPageWikiLink Category:Artificial_intelligence.
- Algorithmic_probability wikiPageWikiLink Category:Probability_interpretations.
- Algorithmic_probability wikiPageWikiLink Epicurus.
- Algorithmic_probability wikiPageWikiLink Hypothesis.
- Algorithmic_probability wikiPageWikiLink Inductive_inference.
- Algorithmic_probability wikiPageWikiLink Inductive_probability.
- Algorithmic_probability wikiPageWikiLink Inductive_reasoning.
- Algorithmic_probability wikiPageWikiLink Information-based_complexity.
- Algorithmic_probability wikiPageWikiLink Invariance_theorem_(algorithmic_probability).
- Algorithmic_probability wikiPageWikiLink Karl_Popper.
- Algorithmic_probability wikiPageWikiLink Kolmogorov_complexity.
- Algorithmic_probability wikiPageWikiLink Mathematical_object.
- Algorithmic_probability wikiPageWikiLink Occams_razor.
- Algorithmic_probability wikiPageWikiLink Probability.
- Algorithmic_probability wikiPageWikiLink Probability_distribution.
- Algorithmic_probability wikiPageWikiLink Ray_Solomonoff.
- Algorithmic_probability wikiPageWikiLink Scholarpedia.
- Algorithmic_probability wikiPageWikiLink Solomonoffs_theory_of_inductive_inference.
- Algorithmic_probability wikiPageWikiLink Universal_Turing_machine.
- Algorithmic_probability wikiPageWikiLink Universality_(philosophy).
- Algorithmic_probability wikiPageWikiLinkText "Algorithmic probability".
- Algorithmic_probability wikiPageWikiLinkText "algorithmic probability".
- Algorithmic_probability date "September 2015".
- Algorithmic_probability hasPhotoCollection Algorithmic_probability.
- Algorithmic_probability reason "According to his wikipedia article, 'Popper is known for his rejection of the classical inductivist views on the scientific method'. Consequently, he didn't give an 'inductive inference theory'.".
- Algorithmic_probability reason "Explain why it is called 'algorithmic', although it can't be computed by any algorithm.".
- Algorithmic_probability wikiPageUsesTemplate Template:Clarify.
- Algorithmic_probability wikiPageUsesTemplate Template:Reflist.
- Algorithmic_probability subject Category:Algorithmic_information_theory.
- Algorithmic_probability subject Category:Artificial_intelligence.
- Algorithmic_probability subject Category:Probability_interpretations.
- Algorithmic_probability hypernym Method.
- Algorithmic_probability type Area.
- Algorithmic_probability type Article.
- Algorithmic_probability type Software.
- Algorithmic_probability type Area.
- Algorithmic_probability type Article.
- Algorithmic_probability comment "In algorithmic information theory, algorithmic (Solomonoff) probability is a mathematical method of assigning a prior probability to a given observation. In a theoretic sense, the prior is universal. It is used in inductive inference theory, and analyses of algorithms.".
- Algorithmic_probability label "Algorithmic probability".
- Algorithmic_probability sameAs アルゴリズム的確率.
- Algorithmic_probability sameAs m.024143.
- Algorithmic_probability sameAs Q4724365.
- Algorithmic_probability sameAs Q4724365.
- Algorithmic_probability wasDerivedFrom Algorithmic_probability?oldid=680371419.
- Algorithmic_probability isPrimaryTopicOf Algorithmic_probability.