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Inductive Inference

1983; Case, Smith

  • Reference work entry
Encyclopedia of Algorithms

  • 185 Accesses

Keywords and Synonyms

Induction; Learning from examples      

Problem Definition

The theory of inductive inference is concerned with the capabilities and limitations of machine learning. Here the learning machine, the concepts to be learned, as well as the hypothesis space are modeled in recursion theoretic terms, based on the framework of identification in the limit [1,8].

Formally, considering recursive functions (mapping natural numbers to natural numbers) as target concepts, a learner (inductive inference machine) is supposed to process, step by step, gradually growing segments of the graph of a target function. In each step, the learner outputs a program in some fixed programming system, where successful learning means that the sequence of programs returned in this process eventually stabilizes on some program actually computing the target function.

Case and Smith [2,3] have proposed several variants of this model in order to study the influence that certain constraints or relaxations...

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Recommended Reading

  1. Blum, L., Blum, M.: Toward a mathematical theory of inductive inference. Inform. Control 28(2), 125–155 (1975)

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  2. Case, J., Smith, C.H.: Anomaly hierarchies of mechanized inductive inference. In: Proceedings of the 10th Symposium on the Theory of Computing, pp. 314–319. ACM, New York (1978)

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  3. Case, J., Smith, C.H.: Comparison of Identification Criteria for Machine Inductive Inference. Theor. Comput. Sci. 25(2), 193–220 (1983)

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  4. Daley, R.P., Smith, C.H.: On the Complexity of Inductive Inference. Inform. Control 69(1–3), 12–40 (1986)

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  5. Freivalds, R., Kinber, E., Smith, C.H.: On the Intrinsic Complexity of Learning. Inform. Comput. 118(2), 208–226 (1995)

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  6. Freivalds, R., Kinber, E., Wiehagen, R.: How inductive inference strategies discover their errors. Inform. Comput. 123(1), 64–71 (1995)

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  7. Freivalds, R., Smith, C.H.: On the Role of Procrastination in Machine Learning. Inform. Comput. 107(2), 237–271 (1993)

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  8. Gold, E.M.: Language identification in the limit. Inform. Control 10(5), 447–474 (1967)

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  9. Kinber, E.B., Stephan, F.: Language Learning from Texts: Mindchanges, Limited Memory, and Monotonicity. Inform. Comput. 123(2), 224–241 (1995)

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  10. Lange, S., Grieser, G., Zeugmann, T.: Inductive inference of approximations for recursive concepts. Theor. Comput. Sci. 348(1), 15–40 (2005)

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  11. Pitt, L.: Inductive inference, DFAs, and computational complexity. In: Analogical and Inductive Inference, 2nd International Workshop, Reinhardsbrunn Castle, GDR. Lecture Notes in Computer Science, vol. 397, pp. 18–44. Springer, Berlin (1989)

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  12. Popper, K.: The Logic of Scientific Discovery. Harper & Row, New York (1959)

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  13. Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967)

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Author information

Authors and Affiliations

  1. Department of Computing Science, University of Alberta, Edmonton, AB, Canada

    Sandra Zilles

Authors
  1. Sandra Zilles
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Zilles, S. (2008). Inductive Inference. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_189

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