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Learning an optimally accurate representation system

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Foundations of Knowledge Representation and Reasoning

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 810))

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Abstract

A default theory can sanction different, mutually incompatible, answers to certain queries. We can identify each such theory with a set of related credulous theories, each of which produces but a single response to each query, by imposing a total ordering on the defaults. Our goal is to identify the credulous theory with optimal “expected accuracy” averaged over the natural distribution of queries in the domain. There are two obvious complications: First, the expected accuracy of a theory depends on the query distribution, which is usually not known. Second, the task of identifying the optimal theory, even given that distribution information, is intractable. This paper presents a method, OptAcc, that side-steps these problems by using a set of samples to estimate the unknown distribution, and by hill-climbing to a local optimum. In particular, given any error and confidence parameters ε, δ > 0, OptAcc produces a theory whose expected accuracy is, with probability at least 1−δ, within ε of a local optimum.

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References

  1. Carlos E. Alchourrón, Peter Gärdenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510–30, 1985.

    Google Scholar 

  2. Mark Boddy and Thomas Dean. Solving time dependent planning problems. Technical report, Brown University, 1988.

    Google Scholar 

  3. Alex Borgida and David Etherington. Hierarchical knowledge bases and efficient disjunctive reasoning. In Proceedings of KR-89, pages 33–43, Toronto, May 1989.

    Google Scholar 

  4. Bruce G. Buchanan, Thomas M. Mitchell, Reid G. Smith, and C. R. Johnson, Jr. Models of learning systems. In Encyclopedia of Computer Science and Technology, volume 11. Dekker, 1978.

    Google Scholar 

  5. B. Bollobás. Random Graphs. Academic Press, 1985.

    Google Scholar 

  6. Gerhard Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of IJCAI-89, pages 1043–48, Detroit, August 1989.

    Google Scholar 

  7. K. Clark. Negation as failure. In H. Gallaire and J. Minker, editors, Logic and Data Bases, pages 293–322. Plenum Press, New York, 1978.

    Google Scholar 

  8. William W. Cohen. Learning from textbook knowledge: A case study. In Proceeding of AAAI-90, 1990.

    Google Scholar 

  9. William W. Cohen. Abductive explanation-based learning: A solution to the multiple inconsistent explanation problems. Machine Learning, 8(2):167–219, March 1992.

    Google Scholar 

  10. Thomas Dean and Mark Boddy. An analysis of time-dependent planning. In Proceedings of AAAI-88, pages 49–54, August 1988.

    Google Scholar 

  11. Mukesh Dalal and David Etherington. Tractable approximate deduction using limited vocabulary. In Proceedings of CSCSI-92, Vancouver, May 1992.

    Google Scholar 

  12. Jon Doyle and Ramesh Patil. Two theses of knowledge representation: Language restrictions, taxonomic classification, and the utility of representation services. Artificial Intelligence, 48(3), 1991.

    Google Scholar 

  13. N. Flann and T. G. Dietterich. A study of explanation-based methods for inductive learning. Machine Learning, 4, 1989.

    Google Scholar 

  14. Peter Gardenfors. Knowledge in Flux: Modeling the Dynamics of the Epistemic States. Bradford Book, MIT Press, Cambridge, MA, 1988.

    Google Scholar 

  15. Russell Greiner and Charles Elkan. Measuring and improving the effectiveness of representations. In Proceedings of IJCAI-91, pages 518–24, Sydney, Australia, August 1991.

    Google Scholar 

  16. Russell Greiner and Igor Jurišica. A statistical approach to solving the EBL utility problem. In Proceedings of AAAI-92, San Jose, 1992.

    Google Scholar 

  17. Russell Greiner and Pekka Orponen. Probably approximately optimal derivation strategies. In J.A. Allen, R. Fikes, and E. Sandewall, editors, Proceedings of KR-91, San Mateo, CA, April 1991. Morgan Kaufmann.

    Google Scholar 

  18. Russell Greiner. Learning near optimal horn approximations. In Proceedings of Knowledge Assimilation Symposium, Stanford, March 1992.

    Google Scholar 

  19. Russell Greiner. Probabilistic hill-climbing: Theory and applications. In Proceedings of CSCSI-92, Vancouver, June 1992.

    Google Scholar 

  20. Russell Greiner. The complexity of computing optimally-accurate default theories. Technical report, Siemens Corporate Research, 1993.

    Google Scholar 

  21. Benjamin Grosof. Generalizing prioritization. In Proceedings of KR-91, pages 289–300, Boston, April 1991.

    Google Scholar 

  22. Russell Greiner and Dale Schuurmans. Learning useful horn approximations. In B. Nebel, C. Rich, and W. Swartout, editors, Proceedings of KR-92, San Mateo, CA, October 1992. Morgan Kaufmann.

    Google Scholar 

  23. David Haussler. Quantifying inductive bias: AI learning algorithms and Valiant's learning framework. Artificial Intelligence, pages 177–221, 1988.

    Google Scholar 

  24. Geoff Hinton. Connectionist learning procedures. Artificial Intelligence, 40(1–3):185–234, September 1989.

    Google Scholar 

  25. David Haussler and Leslie Valiant, editors. Proceedings of the First Workshop on Computational Learning Theory. Morgan Kaufmann, MIT, 1988.

    Google Scholar 

  26. H. Kyburg. The reference class. Philosophy of Science, 50, 1982.

    Google Scholar 

  27. Hector J. Levesque. Foundations of a functional approach to knowledge representation. Artificial Intelligence, 23:155–212, 1984.

    Google Scholar 

  28. R. Loui. Computing reference classes. In AAAI Workshop on Uncertainty. Morgan Kaufmann, St Paul, 1988.

    Google Scholar 

  29. S. Muggleton and W. Buntine. Machine invention of first order predicates by inverting resolution. In Proceedings of IML-88, pages 339–51. Morgan Kaufmann, 1988.

    Google Scholar 

  30. Ryszard S. Michalski, Jaime G. Carbonell, and Thomas M. Mitchell, editors. Machine Learning: An Artificial Intelligence Approach. Tioga Publishing Company, Palo Alto, CA, 1983.

    Google Scholar 

  31. Thomas M. Mitchell. The need for bias in learning generalizations. Technical Report CBM-TR-117, Laboratory for Computer Science Research, May 1980.

    Google Scholar 

  32. Paul Morris. Curing anomalous extensions. In Proceedings of AAAI-87, pages 437–42, Seattle, July 1987.

    Google Scholar 

  33. Pekka Orponen and Russell Greiner. On the sample complexity of finding good search strategies. In Proceedings of COLT-90, pages 352–58, Rochester, August 1990.

    Google Scholar 

  34. Dirk Ourston and Raymond J. Mooney. Changing the rules: A comprehensive approach to theory refinement. In Proceedings of AAAI-90, pages 815–20, 1990.

    Google Scholar 

  35. M. Pazzani. Selecting the best explanation in explanation-based learning. In Proceedings of Symposium on Explanation-Based Learning, Stanford, March 1988.

    Google Scholar 

  36. David Poole, Randy Goebel, and Romas Aleliunas. Theorist: A logical reasoning system for default and diagnosis. Technical Report CS-86-06, Logic Programming and Artificial Intelligence Group, Faculty of Mathematics, University of Waterloo, February 1986.

    Google Scholar 

  37. J. Ross Quinlan. Learning logical definitions from relations. Machine Learning Journal, 5(3):239–66, August 1990.

    Google Scholar 

  38. Raymond Reiter. Nonmonotonic reasoning. In Annual Review of Computing Sciences, volume 2, pages 147–87. Annual Reviews Incorporated, Palo Alto, 1987.

    Google Scholar 

  39. Stuart J. Russell and Benjamin N. Grosof. A declarative approach to bias in concept learning. In Proceedings of AAAI-87, pages 505–10, Seattle, WA, July 1987.

    Google Scholar 

  40. Ehud Shapiro. Algorithmic Program Debugging. MIT Press, 1983.

    Google Scholar 

  41. Lokendra Shastri. Default reasoning in semantic networks: A formalization of recognition and inheritance. Artificial Intelligence, 39:283–355, 1989.

    Google Scholar 

  42. Bart Selman and Henry Kautz. Knowledge compilation using horn approximations. In Proceedings of AAAI-91, pages 904–09, Anaheim, August 1991.

    Google Scholar 

  43. Paul van Arragon. Nested default reasoning with priority levels. In Proceedings of CSCSI-90, pages 77–83, Ottawa, May 1990.

    Google Scholar 

  44. David Vormittag. Evaluating answers to questions, May 1991. Bachelors Thesis, University of Toronto.

    Google Scholar 

  45. Jonathan Wong. Improving the accuracy of a representational system, May 1991. Bachelors Thesis, University of Toronto.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Siemens Corporate Research, 755 College Road East, 08540-6632, Princeton, NJ

    Russell Greiner

  2. Dept. of Computer Science, University of Toronto, M5S 1A4, Toronto, ON, Canada

    Dale Schuurmans

Authors
  1. Russell Greiner
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  2. Dale Schuurmans
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Editor information

Gerhard Lakemeyer Bernhard Nebel

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© 1994 Springer-Verlag Berlin Heidelberg

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Greiner, R., Schuurmans, D. (1994). Learning an optimally accurate representation system. In: Lakemeyer, G., Nebel, B. (eds) Foundations of Knowledge Representation and Reasoning. Lecture Notes in Computer Science, vol 810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58107-3_9

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  • DOI: https://doi.org/10.1007/3-540-58107-3_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58107-9

  • Online ISBN: 978-3-540-48453-0

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