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On Learning Decision Trees with Large Output Domains

By Nader H. Bshouty, Christino Tamon and David K. Wilson


For two disjoint sets of variables, X and Y , and a class of functions C, we define DT (X; Y; C) to be the class of all decision trees over X whose leaves are functions from C over Y . We study the learnability of DT (X; Y; C) using membership and equivalence queries. Boolean decision trees, DT (X; ;; f0; 1g), were shown to be exactly learnable by Bshouty but does this imply the learnability of decision trees that have non-boolean leaves? A simple encoding of all possible leaf values will work provided that the size of C is reasonable. Our investigation involves several cases where simple encoding is not feasible, i.e., when jCj is large. We show how to learn decision trees whose leaves are learnable concepts belonging to a class C, DT (X; Y; C), when the separation between the variables X and Y is known. A simple algorithm for decision trees whose leaves are constants, DT (X; ;; C), is also presented. Each case above requires at least s separate executions of the algorithm d..

Year: 1998
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