Exploiting the Omission of Irrelevant Data

Most learning algorithms work most eeectively when their training data contain completely speciied labeled samples. In many diagnostic tasks, however, the data will include the values of only some of the attributes; we model this as a blocking process that hides the values of those attributes from the learner. While blockers that remove the values of critical attributes can handicap a learner, this paper instead focuses on blockers that remove only irrelevant attribute values, i.e., values that are not needed to classify an instance, given the values of the other unblocked attributes. We rst motivate and formalize this model of \superruous-value blocking," and then demonstrate that these omissions can be useful, by proving that certain classes that seem hard to learn in the general PAC model | viz., decision trees and DNF formulae | are trivial to learn in this setting. We also show that this model can be extended to deal with (1) theory revision (i.e., modifying an existing formula); (2) blockers that occasionally include superruous values or exclude required values; and (3) other corruptions of the training data. This is an extended version of the paper, \Dealing with (Intentionally) Omitted Data: Exploiting Relative Irrelevancies", which appears in working notes of the 1994 AAAI Fall Symposium on \Relevance", New Orleans, November 1994. We gratefully acknowledge receiving helpful comments from R.