Technical Report CIS9110

Authors: G.Y. Benedek and A. Itai
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Abstract: We consider the PAC-learning model first introduced by Valiant, but assume that the distribution is known to the student. The problem addressed here is characterizing when learnability with respect to distribution $D_1$ implies learnability with respect to distribution $D_2$. The answer to the above question depends on the learnability model. If the number of examples need not be bounded by a polynomial, it is sufficient to require that all sets which have zero probability with respect to $D_2$ have zero probability with respect to $D_1$. If the number of examples is required to be polynomial, then the probability with respect to $D_2$ must be bounded by a multiplicative constant from that of $D_1$. More stringent conditions must hold if we insist that every hypothesis consistent with the examples be close to the target. Finally, we address the learnability properties of classes of distributions.
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