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Learning Theory: the Probably Approximately Correct Framework

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Encyclopedia of Systems and Control
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Abstract

In this article, a brief overview is given of one particular approach to machine learning, known as PAC (probably approximately correct) learning theory. A central concept in PAC learning theory is the Vapnik-Chervonenkis (VC) dimension. Finiteness of the VC-dimension is sufficient for PAC learnability, and in some cases, is also necessary. Some directions for future research are also indicated.

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Bibliography

  • Anthony M, Bartlett PL (1999) Neural network learning: theoretical foundations. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Anthony M, Biggs N (1992) Computational learning theory. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Benedek G, Itai A (1991) Learnability by fixed distributions. Theor Comput Sci 86:377–389

    Article  MATH  Google Scholar 

  • Blumer A, Ehrenfeucht A, Haussler D, Warmuth M (1989) Learnability and the Vapnik-Chervonenkis dimension. J ACM 36(4):929–965

    Article  MathSciNet  MATH  Google Scholar 

  • Campi M, Vidyasagar M (2001) Learning with prior information. IEEE Trans Autom Control 46(11):1682–1695

    Article  MathSciNet  MATH  Google Scholar 

  • Devroye L, Györfi L, Lugosi G (1996) A probabilistic theory of pattern recognition. Springer, New York

    Book  MATH  Google Scholar 

  • Gamarnik D (2003) Extension of the PAC framework to finite and countable Markov chains. IEEE Trans Inf Theory 49(1):338–345

    Article  MathSciNet  MATH  Google Scholar 

  • Kearns M, Vazirani U (1994) Introduction to computational learning theory. MIT, Cambridge

    Book  Google Scholar 

  • Kulkarni SR, Vidyasagar M (1997) Learning decision rules under a family of probability measures. IEEE Trans Inf Theory 43(1):154–166

    Article  MathSciNet  MATH  Google Scholar 

  • Meir R (2000) Nonparametric time series prediction through adaptive model selection. Mach Learn 39(1):5–34

    Article  MATH  Google Scholar 

  • Natarajan BK (1991) Machine learning: a theoretical approach. Morgan-Kaufmann, San Mateo

    Google Scholar 

  • van der Vaart AW, Wallner JA (1996) Weak convergence and empirical processes. Springer, New York

    Book  Google Scholar 

  • Vapnik VN (1995) The nature of statistical learning theory. Springer, New York

    Book  MATH  Google Scholar 

  • Vapnik VN (1998) Statistical learning theory. Wiley, New York

    MATH  Google Scholar 

  • Vidyasagar M (1997) A theory of learning and generalization. Springer, London

    MATH  Google Scholar 

  • Vidyasagar M (2003) Learning and generalization: with applications to neural networks. Springer, London

    Book  MATH  Google Scholar 

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Correspondence to Mathukumalli Vidyasagar .

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Vidyasagar, M. (2021). Learning Theory: the Probably Approximately Correct Framework. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, Cham. https://doi.org/10.1007/978-3-030-44184-5_227

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