Abstract
We define a new PAC learning model. In this model, examples are drawn according to the universal distribution m(. ¦ f) of Solomomoff-Levin, where f is the target concept. The consequence is that the simple examples of the target concept have a high probability to be provided to the learning algorithm. We prove an Occam's Razor theorem. We show that the class of poly-term DNF is learnable, and the class of k-reversible languages is learnable from positive data, in this new model.
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References
D. Angluin, Inference of reversible languages, J. Assoc. Comput. Mach. 29 (1982) 741–765.
D. Angluin, Queries and Concept Learning, Machine Learning 2 (1982) 741–765.
G.Benedek and A.Itai, Learnability by fixed ditribution, Proc. 1st ACM Workshop on Computational Learning Theory, (1988) 80–90.
A. Blum, M. Furst, J. Jackson, M. Kearns, Y. Mansour, S. Rudich, Weakly Learning DNF and Characterizing Statistical Query Learning Using Fourier Analysis, Proc. th 26th ACM Symposium on Theory of Computing, (1994) 253–262.
A. Blumer, A. Ehrenfeucht, D. Haussler, and M.K. Warmuth, Occam's razor, Inform. Proc. Lett. 24 (1987) 377–380.
J. Castro, A note on learning decision lists, Report de Recerca, LSI-95-2-R, Dept LSI, UPC, (1995).
D.Haussler, M.Kearns, N.Littlestone and M.Warmuth, Equivalence of models for polynomial learnability, Proc. 1st ACM Workshop on Computational Learning Theory, (1988) 42–55.
M.Kearns, M.Li, L.Pitt and L.G.Valiant, On the learnability of boolean formulae, Proc. 19th ACM Symposium on Theory of Computing, (1987) 285–295.
M. Li and P. Vitányi, Learning simple concepts under simple distributions, SIAM J. Comput. 20 (1991) 911–935.
M.Li and P.Vitányi, An introduction to Kolmogorov complexity and its applications, Texts and Monographs in Computer Science, Springer Verlag, (1993).
B.K.Natarajan, On learning boolean functions, Proc. 19th ACM Symposium on Theory of Computing, (1987) 296–304.
B.K.Natarajan, Machine Learning: a theoretical approach, Morgan Kaufman, (1991).
L.G.Valiant, A theory of the learnable, Comm. ACM., (1984) 1134–1142.
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© 1996 Springer-Verlag Berlin Heidelberg
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Denis, F., D'Halluin, C., Gilleron, R. (1996). PAC learning with simple examples. In: Puech, C., Reischuk, R. (eds) STACS 96. STACS 1996. Lecture Notes in Computer Science, vol 1046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60922-9_20
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DOI: https://doi.org/10.1007/3-540-60922-9_20
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