Back نظرية سولومونوف في الاستدلال الاستقرائي Arabic Teoria da Inferência Indutiva de Solomonoff Portuguese 所罗门诺夫的归纳推理理论 Chinese

Solomonoff's theory of inductive inference

Solomonoff's theory of inductive inference proves that, under its common sense assumptions (axioms), the best possible scientific model is the shortest algorithm that generates the empirical data under consideration. In addition to the choice of data, other assumptions are that, to avoid the post-hoc fallacy, the programming language must be chosen prior to the data[1] and that the environment being observed is generated by an unknown algorithm. This is also called a theory of induction. Due to its basis in the dynamical (state-space model) character of Algorithmic Information Theory, it encompasses statistical as well as dynamical information criteria for model selection. It was introduced by Ray Solomonoff, based on probability theory and theoretical computer science.[2][3][4] 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.

Solomonoff proved that this induction is incomputable (or more precisely, lower semi-computable), but noted that "this incomputability is of a very benign kind", and that it "in no way inhibits its use for practical prediction" (as it can be approximated from below more accurately with more computational resources).[3] It is only "incomputable" in the benign sense that no scientific consensus is able to prove that the best current scientific theory is the best of all possible theories. However, Solomonoff's theory does provide an objective criterion for deciding among the current scientific theories explaining a given set of observations.

Solomonoff's induction naturally formalizes Occam's razor[5][6][7][8][9] by assigning larger prior credences to theories that require a shorter algorithmic description.

  1. ^ Rathmanner, Samuel (3 June 2011). "A Philosophical Treatise of Universal Induction". Entropy. 13 (6): 1076–1136. arXiv:1105.5721. doi:10.3390/e13061076.
  2. ^ Zenil, Hector (2011-02-11). Randomness Through Computation: Some Answers, More Questions. World Scientific. ISBN 978-981-4462-63-1.
  3. ^ a b Solomonoff, Ray J. (2009), Emmert-Streib, Frank; Dehmer, Matthias (eds.), "Algorithmic Probability: Theory and Applications", Information Theory and Statistical Learning, Boston, MA: Springer US, pp. 1–23, doi:10.1007/978-0-387-84816-7_1, ISBN 978-0-387-84816-7, retrieved 2020-07-21
  4. ^ Hoang, Lê Nguyên (2020). The equation of knowledge : from Bayes' rule to a unified philosophy of science (First ed.). Boca Raton, FL. ISBN 978-0-367-85530-7. OCLC 1162366056.{{cite book}}: CS1 maint: location missing publisher (link)
  5. ^ JJ McCall. Induction: From Kolmogorov and Solomonoff to De Finetti and Back to Kolmogorov – Metroeconomica, 2004 – Wiley Online Library.
  6. ^ D Stork. Foundations of Occam's razor and parsimony in learning from ricoh.com – NIPS 2001 Workshop, 2001
  7. ^ A.N. Soklakov. Occam's razor as a formal basis for a physical theory from arxiv.org – Foundations of Physics Letters, 2002 – Springer
  8. ^ Jose Hernandez-Orallo (1999). "Beyond the Turing Test" (PDF). Journal of Logic, Language and Information. 9.
  9. ^ M Hutter. On the existence and convergence of computable universal priors arxiv.org – Algorithmic Learning Theory, 2003 – Springer

Solomonoff's theory of inductive inference

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