TY - GEN

T1 - Learning k-term monotone boolean formulae

AU - Sakai, Yoshifumi

AU - Maruoka, Akira

N1 - Publisher Copyright:
© 1993, Springer Verlag. All rights reserved.

PY - 1993

Y1 - 1993

N2 - Valiant introduced a computational model of learning by examples, and gave a precise definition of learnability based on the model. Since then, much effort has been devoted to characterize learnable classes of concepts on this model. Among such learnable classes is the one, denoted k-term MDNF, consisting of monotone disjunctive normal form formulae with at most k terms. In literature, k-term MDNF is shown to be learnable under the assumption that examples are drawn according to the uniform distribution. In this paper we generalize the result to obtain the statement that k-term MDNF is learnable even if positive examples are drawn according to such distribution that the maximum of the ratio of the probabilities of two positive examples is bounded from above by some polynomial.

AB - Valiant introduced a computational model of learning by examples, and gave a precise definition of learnability based on the model. Since then, much effort has been devoted to characterize learnable classes of concepts on this model. Among such learnable classes is the one, denoted k-term MDNF, consisting of monotone disjunctive normal form formulae with at most k terms. In literature, k-term MDNF is shown to be learnable under the assumption that examples are drawn according to the uniform distribution. In this paper we generalize the result to obtain the statement that k-term MDNF is learnable even if positive examples are drawn according to such distribution that the maximum of the ratio of the probabilities of two positive examples is bounded from above by some polynomial.

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U2 - 10.1007/3-540-57369-0_39

DO - 10.1007/3-540-57369-0_39

M3 - Conference contribution

AN - SCOPUS:84952051945

SN - 9783540573692

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 197

EP - 207

BT - Algorithmic Learning Theory - 3rd Workshop, ALT 1992, Proceedings

A2 - Doshita, Shuji

A2 - Furukawa, Koichi

A2 - Jantke, Klaus P.

A2 - Nishida, Toyaki

PB - Springer Verlag

T2 - 3rd Workshop on Algorithmic Learning Theory, ALT 1992

Y2 - 20 October 1992 through 22 October 1992

ER -