Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Algorithms pp 977–980Cite as

Inductive Inference

  • Reference work entry
  • First Online:

  • 130 Accesses

Years and Authors of Summarized Original Work

  • 1983; Case, Smith

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, 9, 15].

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 initial 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 [3, 4] proposed several variants of this model in order to study the influence that certain...

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   1,599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   1,999.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Recommended Reading

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Case J, Kötzing T (2011) Measuring learning complexity with criteria epitomizers. In: Proceedings of the 28th international symposium on theoretical aspects of computer science, Dortmund. Leibniz international proceedings in informatics, pp 320–331

    Google Scholar 

  3. Case J, Smith CH (1978) Anomaly hierarchies of mechanized inductive inference. In: Proceedings of the 10th symposium on the theory of computing, San Diego. ACM, New York, pp 314–319

    Google Scholar 

  4. Case J, Smith CH (1983) Comparison of identification criteria for machine inductive inference. Theor Comput Sci 25(2):193–220

    Article  MathSciNet  MATH  Google Scholar 

  5. Daley RP, Smith CH (1986) On the complexity of inductive inference. Inf Control 69(1–3):12–40

    Article  MathSciNet  MATH  Google Scholar 

  6. Freivalds R, Kinber E, Smith CH (1995) On the intrinsic complexity of learning. Inf Comput 118(2):208–226

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Freivalds R, Smith CH (1993) On the role of procrastination in machine learning. Inf Comput 107(2):237–271

    Article  MathSciNet  MATH  Google Scholar 

  9. Gold EM (1967) Language identification in the limit. Inf Control 10(5):447–474

    Article  MATH  Google Scholar 

  10. Kinber EB, Stephan F (1995) Language learning from texts: mindchanges, limited memory, and monotonicity. Inf Comput 123(2):224–241

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  12. Pitt L (1989) Inductive inference, DFAs, and computational complexity. In: Analogical and inductive inference, 2nd international workshop, Reinhardsbrunn Castle, GDR. Lecture notes in computer science, vol 397. Springer, Berlin, pp 18–44

    Google Scholar 

  13. Popper K (1959) The logic of scientific discovery. Harper & Row, New York

    MATH  Google Scholar 

  14. Rogers H (1967) Theory of recursive functions and effective computability. McGraw-Hill, New York

    MATH  Google Scholar 

  15. Zeugmann T, Zilles S (2008) Learning recursive functions: a survey. Theor Comput Sci 397:4–56

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Regina, 3737 Wascana Parkway, S4S 0A2, Regina, SK, Canada

    Sandra Zilles

Authors
  1. Sandra Zilles
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sandra Zilles .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this entry

Cite this entry

Zilles, S. (2016). Inductive Inference. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_189

Download citation

Publish with us

Policies and ethics

Search

Navigation