PAC learning with irrelevant attributes
Dhagat, A.; Hellerstein, L.
Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on
Volume , Issue , 20-22 Nov 1994 Page(s):64 - 74
Digital Object Identifier 10.1109/SFCS.1994.365704
Summary:We consider the problem of learning in the presence of irrelevant
attributes in Valiant's PAC model (1984). In the PAC model, the goal of
the learner is to produce an approximately correct hypothesis from
random sample data. If the number of relevant attributes in the target
function is small, it may be desirable to produce a hypothesis that also
depends on only a small number of variables. Haussler (1988) previously
considered the problem of learning monomials of a small number of
variables. He showed that the greedy set cover approximation algorithm
can be used as a polynomial-time Occam algorithm for learning monomials
on r of n variables. A outputs a monomial on r(ln q+1) variables, where
q is the number of negative examples in the sample. We extend this
result by showing that there is a polynomial-time Occam algorithm for
learning k-term DNF formulas depending on r of n variables that outputs
a DNF formula depending on O(rklogkq) variables,
where q is the number of negative examples in the sample. We also give a
polynomial-time Occam algorithm for learning decision lists (sometimes
called 1-decision lists) with k alternations
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