Abstract

We investigate learnability in the PAC model when the data used for learning, attributes and labels, is either corrupted or incomplete. In order to prove our main results, we define a new complexity measure on statistical query (SQ) learning algorithms. The view of an SQ algorithm is the maximumover all queries in the algorithm, of the number of input bits on which the query depends. We show that a restricted view SQ algorithm for a class is a general sufficient condition for learnability in both the models of attribute noise and covered (or missing) attributes. We further show that since the algorithms in question are statistical, they can also simultaneously tolerate classification noise. Classes for which these results hold, and can therefore be learned with simultaneous attribute noise and classification noise, include k-DNF, k-term-DNF by DNF representations, conjunctions with few relevant variables, and over the uniform distribution, decision lists. These noise models are the fi...

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