Abstract
We study the learnability from examples of boolean formulae assuming that the examples satisfy a uniform distribution assumption. We analyze the requirements of known algorithms (upper and lower bounds) under uniform distribution and we propose a new combinatorial measure in order to characterize the complexity of boolean formulae.
Work partially supported by Italian project MPI ‘Algoritmi e Structure di Calcolo’.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
6 References
A.Blumer,A.Ehrenfeucht,D.Haussler,M.Warmuth Classifying learnable geometric concepts with the Vapnik-Chervonenkis dimension Proc. 18th Acm Symposium on Theory of Computing (1987).
P.Berman,R.Roos Learning one-counter languages in polynomial time Proc. 28th Symposium on Foundations of Computer Science (1987).
A.Ehrenfeucht, D.Haussler,M.Kearns,L.Valiant A general lower bound on the number of examples needed for learning Information and Computation (1988).
W.Feller An introduction to probability theory and its applications Vol.1 Wiley and Sons (1971).
D.Haussler Quantifying inductive bias: AI learning and Valiant's learning framework Artificial Intelligence, 36 (1988).
M.Kearns,M.Li,L.Pitt,L.G.Valiant On the learnability of boolean formulae Proc.19th Acm Symposium on Theory of Computing (1987).
N.Linial,Y.Mansour,R.L.Rivest Results on learnability and Vapnik Chervonenkis dimension Proc. 29th Symposium on Foundations of Computer Science (1988).
N.Littlestone Learning quickly when irrelevant attributes abound: a new linear threshold algorithm Machine learning 2,(4) (1988).
T.M.Mitchell Generalization as search Artificial Intelligence, 18 (1982).
B.K.Natarajan On learning boolean functions Proc. 19th Symposium on Theory of Computing (1987).
L.G.Valiant A theory of learnable Comm.Acm, 27,(11) (1984).
V.Vapnik,A.Y.Chervonenkis On the uniform convergence of relative frequencies of events to their probabilities Theor. Prob. and Appl., 16, (2) (1971).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Marchetti-Spaccamela, A., Protasi, M. (1989). Learning under uniform distribution. In: Csirik, J., Demetrovics, J., Gécseg, F. (eds) Fundamentals of Computation Theory. FCT 1989. Lecture Notes in Computer Science, vol 380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51498-8_32
Download citation
DOI: https://doi.org/10.1007/3-540-51498-8_32
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51498-5
Online ISBN: 978-3-540-48180-5
eBook Packages: Springer Book Archive