Book ChapterDOI
On the tractability of learning from incomplete theories
Sridhar Mahadevan,Prasad Tadepalli +1 more
- pp 235-241
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An in-depth analysis of the tractability of learning functions from determinations, a particular form of incomplete domain theory, and introduces the notion of “exceptions,” which is used to identify sufficient conditions for the learnability of function families consistent with partial and extended determinations.Abstract:
One well-known limitation of the explanation-based approach to concept learning is the need for a domain theory strong enough to deductively entail training examples of the concept. As such a theory may be unavailable in many situations, the problem of learning from incomplete domain theories must be addressed. The aim of this paper is to use the Valiant/Natarajan theoretical formalizations of concept learning to study the tractability of learning from incomplete domain theories. In particular, we present an in-depth analysis of the tractability of learning functions from determinations , a particular form of incomplete domain theory[3]. We show that only two of the five function families consistent with the five total determinations are polynomial-time learnable. We introduce the notion of “exceptions, and use it to identify sufficient conditions for the learnability of function families consistent with partial and extended determinations. While our results are specific to determinations, we believe that the underlying approach can be used to analyze other forms of incomplete theories.read more
Citations
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References
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Proceedings ArticleDOI
A theory of the learnable
TL;DR: This paper regards learning as the phenomenon of knowledge acquisition in the absence of explicit programming, and gives a precise methodology for studying this phenomenon from a computational viewpoint.
Journal ArticleDOI
Explanation-based generalization: a unifying view
TL;DR: This paper proposed a general, domain-independent mechanism, called EBG, that unifies previous approaches to explanation-based generalization, which is illustrated in the context of several example problems, and used to contrast several existing systems for explanation based generalization.
Learning Functions from Examples
TL;DR: A theorem is proved identifying the most general conditions under which a family of functions can be efficiently learned from examples, and strong evidence against the existence of efficient algorithms for learning the regular functions and the polynomial time computable functions is presented.