Learning Probabilistic Read-Once Formulas on Product Distributions

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Learning Probabilistic Read-Once Formulas on Product Distributions
Abstract. This paper presents a polynomial-time algorithm for inferring a probabilistic generalization of the class of read-once Boolean formulas over the usual basis {AND,OR,NOT}. The algorithm effectively infers a good approximation of the target formula when provided with random examples which are chosen according to any product distribution, i.e., any distribution in which the setting of each input bit is chosen independently of the settings of the other bits. Since the class of formulas considered includes ordinary read-once Boolean formulas, our result shows that such formulas are PAC learnable (in the sense of Valiant) against any product distribution (for instance, against the uniform distribution). Further, this class of probabilistic formulas includes read-once formulas whose behavior has been corrupted by large amounts of random noise. Such noise may affect the formula's output ("misclassification noise"), the input bits ("attribute noise"), or it ma...
Robert E. Schapire
Added 27 Aug 2010
Updated 27 Aug 2010
Type Conference
Year 1991
Where COLT
Authors Robert E. Schapire
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