Skip to main content

Connections Between Inductive Inference and Machine Learning

  • Reference work entry
  • First Online:
  • 230 Accesses

Abstract

Inductive inference is a branch of computational learning theory which deals with learning in the limit. Though this topic deals with mostly theoretical work, it has provided some results which can be of use to practical machine learning. Some of these works include the work multitask or context-sensitive learning, learnability of elementary formal systems, behavioral cloning, learning to coordinate, geometrical clustering, and so on. The results in these areas also often give insights into limitations of science.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   699.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   949.99
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

  • Ambainis A, Case J, Jain S, Suraj M (2004) Parsimony hierarchies for inductive inference. J Symb Logic 69:287–328

    Article  MathSciNet  MATH  Google Scholar 

  • Angluin D, Gasarch W, Smith C (1989) Training sequences. Theor Comput Sci 66(3):255–272

    Article  MathSciNet  MATH  Google Scholar 

  • Angluin D (1980) Finding patterns common to a set of strings. J Comput Syst Sci 21:46–62

    Article  MathSciNet  MATH  Google Scholar 

  • Arikawa S, Shinohara T, Yamamoto A (1992) Learning elementary formal systems. Theor Comput Sci 95:97–113

    Article  MathSciNet  MATH  Google Scholar 

  • Bain M, Sammut C (1999) A framework for behavioural cloning. In: Furakawa K, Muggleton S, Michie D (eds) Machine intelligence, vol 15. Oxford University Press, Oxford

    Google Scholar 

  • Baluja S, Pomerleau D (1995) Using the representation in a neural network’s hidden layer for task specific focus of attention. Technical report CMU-CS-95-143, School of Computer Science, CMU, May 1995. Appears in proceedings of the 1995 IJCAI

    Google Scholar 

  • Bartlett P, Ben-David S, Kulkarni S (1996) Learning changing concepts by exploiting the structure of change. In: Proceedings of the ninth annual conference on computational learning theory, Desenzano del Garda. ACM Press, New York

    Book  MATH  Google Scholar 

  • Bartlmae K, Gutjahr S, Nakhaeizadeh G (1997) Incorporating prior knowledge about financial markets through neural multitask learning. In: Refenes APN, Burgess AN, Moody JE (eds) Decision technologies for computational finance. Proceedings of the fifth international conference on computational finance. Kluwer Academic, pp 425–432

    Google Scholar 

  • Bārzdiņš J (1974a) Inductive inference of automata, functions and programs. In: Proceedings of the international congress of mathematicians, Vancouver, pp 771–776

    Google Scholar 

  • Bārzdiņš J (1974b) Two theorems on the limiting synthesis of functions. In: Theory of algorithms and programs, vol 210. Latvian State University, Riga, pp 82–88

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Blum A, Chalasani P (1992) Learning switching concepts. In: Proceedings of the fifth annual conference on computational learning theory, Pittsburgh. ACM Press, New York, pp 231–242

    Google Scholar 

  • Bratko I, Muggleton S (1995) Applications of inductive logic programming. Commun ACM 38(11):65–70

    Article  Google Scholar 

  • Bratko I, Urbančič T, Sammut C (1998) Behavioural cloning of control skill. In: Michalski RS, Bratko I, Kubat M (eds) Machine learning and data mining: methods and applications. Wiley, New York, pp 335–351

    Google Scholar 

  • Brazma A, Ukkonen E, Vilo J (1996) Discovering unbounded unions of regular pattern languages from positive examples. In: Proceedings of the seventh international symposium on algorithms and computation (ISAAC’96). Lecture notes in computer science, vol 1178. Springer, Berlin, pp 95–104

    Google Scholar 

  • Breiman L (1996) Bagging predictors. Mach Learn 24(2):123–140

    MATH  Google Scholar 

  • Breiman L (2001) Random forests. Mach Learn 45(1):5–32

    Article  MATH  Google Scholar 

  • Caruana R (1993) Multitask connectionist learning. In: Proceedings of the 1993 connectionist models summer school. Lawrence Erlbaum, Hillsdale, pp 372–379

    Google Scholar 

  • Caruana R (1996) Algorithms and applications for multitask learning. In: Proceedings 13th international conference on machine learning. Morgan Kaufmann, San Francisco, pp 87–95

    Google Scholar 

  • Case J (1994) Infinitary self-reference in learning theory. J Exp Theor Artif Intell 6:3–16

    Article  MATH  Google Scholar 

  • Case J (1999) The power of vacillation in language learning. SIAM J Comput 28(6):1941–1969

    Article  MathSciNet  MATH  Google Scholar 

  • Case J (2007) Directions for computability theory beyond pure mathematical. In: Gabbay D, Goncharov S, Zakharyaschev M (eds) Mathematical problems from applied logic II. New logics for the twenty-first century. International mathematical series, vol 5. Springer, New York

    Google Scholar 

  • Case J, Kötzing T (2009) Difficulties in forcing fairness of polynomial time inductive inference. In: Gavalda R, Lugosi G, Zeugmann T, Zilles S (eds) 20th international conference on algorithmic learning theory (ALT’09). LNAI, vol 5809. Springer, Berlin, pp 263–277

    Chapter  Google Scholar 

  • Case J, Lynes C (1982) Machine inductive inference and language identification. In: Nielsen M, Schmidt E (eds) Proceedings of the 9th international colloquium on automata, languages and programming. Lecture notes in computer science, vol 140. Springer, Berlin, pp 107–115

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Case J, Suraj M (2007) Weakened refutability for machine learning of higher order definitions 2007. Working paper for eventual journal submission

    Google Scholar 

  • Case J, Jain S, Kaufmann S, Sharma A, Stephan F (2001) Predictive learning models for concept drift (special issue for ALT’98). Theor Comput Sci 268:323–349

    Article  MATH  Google Scholar 

  • Case J, Jain S, Lange S, Zeugmann T (1999) Incremental concept learning for bounded data mining. Inf Comput 152:74–110

    Article  MathSciNet  MATH  Google Scholar 

  • Case J, Jain S, Montagna F, Simi G, Sorbi A (2005) On learning to coordinate: random bits help, insightful normal forms, and competency isomorphisms (special issue for selected learning theory papers from COLT’03, FOCS’03, and STOC’03). J Comput Syst Sci 71(3):308–332

    Article  MATH  Google Scholar 

  • Case J, Jain S, Martin E, Sharma A, Stephan F (2006) Identifying clusters from positive data. SIAM J Comput 36(1):28–55

    Article  MathSciNet  MATH  Google Scholar 

  • Case J, Jain S, Ott M, Sharma A, Stephan F (2000) Robust learning aided by context (special issue for COLT’98). J Comput Syst Sci 60:234–257

    Article  MATH  Google Scholar 

  • Case J, Jain S, Sharma A (1996) Machine induction without revolutionary changes in hypothesis size. Inf Comput 128:73–86

    Article  MathSciNet  MATH  Google Scholar 

  • Case J, Jain S, Stephan F, Wiehagen R (2004) Robust learning – rich and poor. J Comput Syst Sci 69(2):123–165

    Article  MathSciNet  MATH  Google Scholar 

  • Case J, Ott M, Sharma A, Stephan F (2002) Learning to win process-control games watching gamemasters. Inf Comput 174(1):1–19

    Article  MathSciNet  MATH  Google Scholar 

  • Cenzer D, Remmel J (1992) Recursively presented games and strategies. Math Soc Sci 24:117–139

    Article  MathSciNet  MATH  Google Scholar 

  • Chen K (1982) Tradeoffs in the inductive inference of nearly minimal size programs. Inf Control 52:68–86

    Article  MathSciNet  MATH  Google Scholar 

  • de Garis H (1990a) Genetic programming: building nanobrains with genetically programmed neural network modules. In: IJCNN: international joint conference on neural networks, vol 3. IEEE Service Center, Piscataway, pp 511–516

    Google Scholar 

  • deGarisH(1990b)Geneticprogramming:modularneuralevolutionforDarwin machines. In: Caudill M (ed) IJCNN-90-WASH DC; international joint conferenceonneuralnetworks,vol 1.LawrenceErlbaumAssociates, Hillsdale, pp 194–197

    Google Scholar 

  • de Garis H (1991) Genetic programming: building artificial nervous systems with genetically programmed neural network modules. In: Soušek B, The IRIS group (eds) Neural and intelligenct systems integeration: fifth and sixth generation integerated reasoning information systems, Chap. 8 Wiley, New York, pp 207–234

    Google Scholar 

  • Devaney M, Ram A (1994) Dynamically adjusting concepts to accommodate changing contexts. In: Kubat M, Widmer G (eds) Proceedings of the ICML-96 pre-conference workshop on learning in context-sensitive domains, Bari. Journal submission

    Google Scholar 

  • Dietterich T, Hild H, Bakiri G (1995) A comparison of ID3 and backpropogation for English text-tospeech mapping. Mach Learn 18(1):51–80

    Google Scholar 

  • Fahlman S (1991) The recurrent cascade-correlation architecture. In: Lippmann R, Moody J, Touretzky D (eds) Advances in neural information processing systems, vol 3. Morgan Kaufmann Publishers, San Mateo, pp 190–196

    Google Scholar 

  • Freivalds R (1975) Minimal Gödel numbers and their identification in the limit. Lecture notes in computer science, vol 32. Springer, Berlin, pp 219–225

    Google Scholar 

  • Freund Y, Mansour Y (1997) Learning under persistent drift. In: Ben-David S, (ed) Proceedings of the third European conference on computational learning theory (EuroCOLT’97). Lecture notes in artificial intelligence, vol 1208. Springer, Berlin, pp 94–108

    Google Scholar 

  • Fulk M (1990) Robust separations in inductive inference. In: Proceedings of the 31st annual symposium on foundations of computer science. IEEE Computer Society, St. Louis, pp 405–410

    Google Scholar 

  • Harding S (ed) (1976) Can theories be refuted? Essays on the Duhem-Quine thesis. Kluwer Academic Publishers, Dordrecht

    MATH  Google Scholar 

  • Helmbold D, Long P (1994) Tracking drifting concepts by minimizing disagreements. Mach Learn 14:27–46

    MATH  Google Scholar 

  • Hildebrand F (1956) Introduction to numerical analysis. McGraw-Hill, New York

    MATH  Google Scholar 

  • Jain S (1999) Robust behaviorally correct learning. Inf Comput 153(2):238–248

    Article  MathSciNet  MATH  Google Scholar 

  • Jain S, Sharma A (1997) Elementary formal systems, intrinsic complexity, and procrastination. Inf Comput 132:65–84

    Article  MathSciNet  MATH  Google Scholar 

  • Jain S, Sharma A (2002) Mind change complexity of learning logic programs. Theor Comput Sci 284(1):143–160

    Article  MathSciNet  MATH  Google Scholar 

  • Jain S, Osherson D, Royer J, Sharma A (1999) Systems that learn: an introduction to learning theory, 2nd edn. MIT Press, Cambridge, MA

    Google Scholar 

  • Jain S, Smith C, Wiehagen R (2001) Robust learning is rich. J Comput Syst Sci 62(1):178–212

    Article  MathSciNet  MATH  Google Scholar 

  • Kilpeläinen P, Mannila H, Ukkonen E (1995) MDL learning of unions of simple pattern languages from positive examples. In: Vitányi P (ed) Computational learning theory, second European conference, EuroCOLT’95. Lecture notes in artificial intelligence, vol 904. Springer, Berlin, pp 252–260

    Chapter  Google Scholar 

  • Kinber E (1977) On a theory of inductive inference. Lecture notes in computer science, vol 56. Springer, Berlin, pp 435–440

    Google Scholar 

  • Kinber E, Smith C, Velauthapillai M, Wiehagen R (1995) On learning multiple concepts in parallel. J Comput Syst Sci 50:41–52

    Article  MathSciNet  MATH  Google Scholar 

  • Krishna Rao M (1996) A class of prolog programs inferable from positive data. In: Arikawa A, Sharma A (eds) Seventh international conference on algorithmic learning theory (ALT’ 96). Lecture notes in artificial intelligence, vol 1160. Springer, Berlin, pp 272–284

    Chapter  Google Scholar 

  • Krishna Rao M (2000) Some classes of prolog programs inferable from positive data (Special Issue for ALT’96). Theor Comput Sci A 241:211–234

    Article  MathSciNet  Google Scholar 

  • Krishna Rao M (2004) Inductive inference of term rewriting systems from positive data. In: Ben-David S, Case J, Maruoka A (eds) Algorithmic learning theory: fifteenth international conference (ALT’2004). Lecture notes in artificial intelligence, vol 3244. Springer, Berlin, pp 69–82

    Chapter  Google Scholar 

  • Krishna Rao M (2005) A class of prolog programs with non-linear outputs inferablefrompositivedata.In:JainS,SimonHU,TomitaE(eds)Algorithmic learningtheory:sixteenthinternationalconference(ALT’2005).Lecturenotes in artificial intelligence, vol 3734. Springer, Berlin, pp 312–326

    Google Scholar 

  • Krishna Rao M, Sattar A (1998) Learning from entailment of logic programs with local variables. In: Richter M, Smith C, Wiehagen R, Zeugmann T (eds) Ninth international conference on algorithmic learning theory (ALT’98). Lecture notes in artificial intelligence, vol 1501. Springer, Berlin, pp 143–157

    Chapter  Google Scholar 

  • Kubat M (1992) A machine learning based approach to load balancing in computer networks. Cybern Syst 23:389–400

    Article  Google Scholar 

  • Kummer M, Ott M (1996) Learning branches and learning to win closed recursive games. In: Proceedings of the ninth annual conference on computational learning theory, Desenzano del Garda. ACM Press, New York

    Google Scholar 

  • Lange S, Wiehagen R (1991) Polynomial time inference of arbitrary pattern languages. New Gener Comput 8:361–370

    Article  MATH  Google Scholar 

  • Lavrač N, Džeroski S (1994) Inductive logic programming: techniques and applications. Ellis Horwood, New York

    MATH  Google Scholar 

  • Maler O, Pnueli A, Sifakis J (1995) On the synthesis of discrete controllers for timed systems. In: Proceedings of the annual symposium on the theoretical aspects of computer science. LNCS, vol 900. Springer, Berlin, pp 229–242

    Google Scholar 

  • Matwin S, Kubat M (1996) The role of context in concept learning. In: Kubat M, Widmer G (eds) Proceedings of the ICML-96 pre-conference workshop on learning in context-sensitive domains, Bari, pp 1–5

    Google Scholar 

  • Maye A, Hsieh C, Sugihara G, Brembs B (2007) Order in spontaneous behavior. PLoS One, May 2007. http://brembs.net/spontaneous/

  • Mishra N, Ron D, Swaminathan R (2004) A new conceptual clustering framework. Mach Learn 56(1–3):115–151

    Article  MATH  Google Scholar 

  • Mitchell T (1997) Machine learning. McGraw Hill, New York

    MATH  Google Scholar 

  • Mitchell T, Caruana R, Freitag D, McDermott J, Zabowski D (1994) Experience with a learning, personal assistant. Commun ACM 37:80–91

    Article  Google Scholar 

  • Montagna F, Osherson D (1999) Learning to coordinate: a recursion theoretic perspective. Synthese 118:363–382

    Article  MathSciNet  MATH  Google Scholar 

  • Muggleton S, De Raedt L (1994) Inductive logic programming: theory and methods. J Logic Program 19/20:669–679

    MathSciNet  MATH  Google Scholar 

  • Odifreddi P (1999) Classical recursion theory, vol II. Elsivier, Amsterdam

    MATH  Google Scholar 

  • Osherson D, Stob M, Weinstein S (1986) Systems that learn: an introduction to learning theory for cognitive and computer scientists. MIT Press, Cambridge, MA

    Google Scholar 

  • Ott M, Stephan F (2002) Avoiding coding tricks by hyperrobust learning. Theor Comput Sci 284(1):161–180

    Article  MathSciNet  MATH  Google Scholar 

  • Pitt L, Reinke R (1988) Criteria for polynomial-time (conceptual) clustering. Mach Learn 2:371–396

    Google Scholar 

  • Popper K (1992) Conjectures and refutations: the growth of scientific knowledge. Basic Books, New York

    Google Scholar 

  • Pratt L, Mostow J, Kamm C (1991) Direct transfer of learned information among neural networks. In: Proceedings of the 9th national conference on artificial intelligence (AAAI-91), Anaheim. AAAI press, Menlo Park

    Google Scholar 

  • Rogers H (1987) Theory of recursive functions and effective computability. McGraw Hill, New York. (Reprinted, MIT Press, 1987)

    Google Scholar 

  • Salomaa A (1994a) Patterns (The formal language theory column). EATCS Bull 54:46–62

    Google Scholar 

  • Salomaa A (1994b) Return to patterns (The formal language theory column). EATCS Bull 55:144–157

    Google Scholar 

  • Sejnowski T, Rosenberg C (1986) NETtalk: a parallel network that learns to read aloud. Technical report JHU-EECS-86-01, Johns Hopkins University

    Google Scholar 

  • Shimozono S, Shinohara A, Shinohara T, Miyano S, Kuhara S, Arikawa S (1994) Knowledge acquisition from amino acid sequences by machine learning system BONSAI. Trans Inf Process Soc Jpn 35:2009–2018

    Google Scholar 

  • Shinohara T (1983) Inferring unions of two pattern languages. Bull Inf Cybern 20:83–88

    MathSciNet  MATH  Google Scholar 

  • Shinohara T, Arikawa A (1995) Pattern inference. In: Jantke KP, Lange S (eds) Algorithmic learning for knowledge-based systems. Lecture notes in artificial intelligence, vol 961. Springer, Berlin, pp 259–291

    Chapter  Google Scholar 

  • Smullyan R (1961) Theory of formal systems. Annals of mathematics studies, vol 47). Princeton University Press, Princeton

    Google Scholar 

  • Šuc D (2003) Machine reconstruction of human control strategies. Frontiers in artificial intelligence and applications, vol 99. IOS Press, Amsterdam

    Google Scholar 

  • Thomas W (1995) On the synthesis of strategies in infinite games. In: Proceedings of the annual symposium on the theoretical aspects of computer science. LNCS, vol 900. Springer, Berlin, pp 1–13

    Google Scholar 

  • Thrun S (1996) Is learning the n-th thing any easier than learning the first? In: Advances in neural information processing systems, vol 8. Morgan Kaufmann, San Mateo

    Google Scholar 

  • Thrun S, Sullivan J (1996) Discovering structure in multiple learning tasks: the TC algorithm. In: Proceedings of the thirteenth international conference on machine learning (ICML-96). Morgan Kaufmann, San Francisco, pp 489–497

    Google Scholar 

  • Tsung F, Cottrell G (1989) A sequential adder using recurrent networks. In: IJCNN-89-WASHINGTON DC: international joint conference on neural networks, 18–22 June, vol 2. IEEE Service Center, Piscataway, pp 133–139

    Google Scholar 

  • Waibel A (1989a) Connectionist glue: modular design of neural speech systems. In: Touretzky D, Hinton G, Sejnowski T (eds) Proceedings of the 1988 connectionist models summer school. Morgan Kaufmann, San Mateo, pp 417–425

    Google Scholar 

  • Waibel A (1989b) Consonant recognition by modular construction of large phonemic time-delay neural networks. In: Touretzky DS (ed) Advances in neural information processing systems I. Morgan Kaufmann, San Mateo, pp 215–223

    Google Scholar 

  • Wallace C (2005) Statistical and inductive inference by minimum message length. Information science and statistics. Springer, New York. Posthumously published

    Google Scholar 

  • Wallace C, Dowe D (1999) Minimum message length and Kolmogorov complexity (special issue on Kolmogorov complexity). Comput J 42(4):123–155. http://comjnl.oxfordjournals.org/cgi/reprint/42/4/270

  • Widmer G, Kubat M (1996) Learning in the presence of concept drift and hidden contexts. Mach Learn 23:69–101

    Google Scholar 

  • Wiehagen R (1976) Limes-Erkennung rekursiver Funktionen durch spezielle Strategien. Electronische Informationverarbeitung und Kybernetik 12: 93–99

    MathSciNet  MATH  Google Scholar 

  • Wiehagen R, Zeugmann T (1994) Ignoring data may be the only way to learn efficiently. J Exp Theor Artif Intell 6:131–144

    Article  MATH  Google Scholar 

  • Wright K (1989) Identification of unions of languages drawn from an identifiable class. In: Rivest R, Haussler D, Warmuth M (eds) Proceedings of the second annual workshop on computational learning theory, Santa Cruz. Morgan Kaufmann Publishers, San Mateo, pp 328–333

    Chapter  Google Scholar 

  • Wrobel S (1994) Concept formation and knowledge revision. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  • Zeugmann T (1986) On Bārzdiņš’ conjecture. In: Jantke KP (ed) Proceedings of the international workshop on analogical and inductive inference. Lecture notes in computer science, vol 265. Springer, Berlin, pp 220–227

    Chapter  Google Scholar 

  • Zeugmann T (1998) Lange and Wiehagen’s pattern language learning algorithm: an average case analysis with respect to its total learning time. Ann Math Artif Intell 23:117–145

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to John Case .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Science+Business Media New York

About this entry

Cite this entry

Case, J., Jain, S. (2017). Connections Between Inductive Inference and Machine Learning. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7687-1_52

Download citation

Publish with us

Policies and ethics