Learning with confidence
Herein we investigate learning in the limit where confidence in the current conjecture accrues with time. Confidence levels are given by rational numbers between 0 and 1. The traditional requirement that for learning in the limit is that a device must converge (in the limit) to a correct answer. We further demand that the associated confidence in the answer (monotonically) approach 1 in the limit. In addition to being a more realistic model of learning, our new notion turns out to be a more powerful as well. In addition, we give precise characterizations of the classes of functions that are learnable in our new model(s).
KeywordsProgramming System Recursive Function Inductive Inference Output Sequence Output Program
Unable to display preview. Download preview PDF.
- [AS87]D. Angluin and C. H. Smith. Inductive inference. In S. Shapiro, editor, Encyclopedia of Artificial Intelligence, pages 409–418. John Wiley and Sons Inc., 1987.Google Scholar
- [Car52]R. Carnap. The Continuum of Inductive Methods. The University of Chicago Press, Chicago, Illinois, 1952.Google Scholar
- [Fre75]R. V. Freivalds. Minimal gödel numbers and their identification in the limit. Lecture Notes in Computer Science, 32:219–225, 1975.Google Scholar
- [Fre90]R. Freivalds. Inductive inference of minimal size programs. In M. Fulk and J. Case, editors, Proceedings of the third Annual Workshop on Computational Learning Theory, pages 1–20. Morgan Kaufman, 1990.Google Scholar
- [Fre91]R. Freivalds. Inductive inference of recursive functions: Qualitative theory. In J. Bārzdins and D. Bjørner, editors, Baltic Computer Science, pages 77–110. Springer Verlag, 1991. Lecture Notes in Computer Science, Vol. 502.Google Scholar
- [Fri58]R. Friedberg. Three theorems on recursive enumeration. Journal of Symbolic Logic, 23:309–316, 1958.Google Scholar
- [G65]K. Gödel. On undecidable propositions of formal mathematical systems. In M. Davis, editor, The Undecidable, pages 39–73. Raven Press, Hewlett, N.Y., 1965.Google Scholar
- [Kin77]E. B. Kinber. On identification in the limit of minimal numbers for functions of effectively enumerable classes. In Barzdins, editor, Theory Of Algorithms and Programs, number 3, pages 35–56. Latvian State University, Riga, U.S.S.R., 1977.Google Scholar
- [MY78]M. Machtey and P. Young. An Introduction to the General Theory of Algorithms. North-Holland, New York, 1978.Google Scholar
- [Smi94]C. Smith. A Recursive Introduction to the Theory of Computation. Springer-Verlag, 1994.Google Scholar