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Learning decision trees from random examples. (English) Zbl 0679.68157
Summary: We define the rank of a decision tree and show that for any fixed r, the class of all decision trees of rank at most r on n Boolean variables is learnable from random examples in time polynomial in n and linear in 1/\(\epsilon\) and log(1/\(\delta)\), where \(\epsilon\) is the accuracy parameter and \(\delta\) is the confidence parameter. Using a suitable encoding of variables, Rivest’s polynomial learnability result for decision lists can be interpreted as a special case of this result for rank 1. As another corollary, we show that decision trees on n Boolean variables of size polynomial in n are learnable from random examples in time linear in \(n^{O(\log n)}\), 1/\(\epsilon\), and log(1/\(\delta)\). As a third corollary, we show that Boolean functions that have polynomial size DNF expressions for both their positive and their negtive instances are learnable from random examples in time linear in \(n^{O((\log n)^ 2)}\), 1/\(\epsilon\), and log(1/\(\delta)\).

MSC:
68T05 Learning and adaptive systems in artificial intelligence
90B50 Management decision making, including multiple objectives
05C05 Trees
06E30 Boolean functions
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