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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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##### References:
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