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The main points of this chapter include: In contrast to purely inductive learning methods that seek a hypothesis to fit the training data, purely analytical learning methods seek a hypothesis
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that fits the learner's prior knowledge and covers the training examples Humans often make use of prior knowledge to guide the formation of new hypotheses This chapter examines purely analytical learning methods The next chapter examines combined inductive-analytical learning Explanation-based learning is a form of analytical learning in which the learner processes each novel training example by (1) explaining the observed target value for this example in terms of the domain theory, (2) analyzing this explanation to determine the general conditions under which the explanation holds, and (3) refining its hypothesis to incorporate these general conditions PROLOG-EBG an explanation-based learning algorithm that uses first-order is Horn clauses to represent both its domain theory and its learned hypotheses In PROLOG-EBG explanation is a PROLOG an proof, and the hypothesis extracted from the explanation is the weakest preimage of this proof As a result, the hypotheses output by PROLOG-EBG follow deductively from its domain theory Analytical learning methods such as PROLOG-EBG construct useful intermediate features as a side effect of analyzing individual training examples This analytical approach to feature generation complements the statistically based generation of intermediate features (eg, hidden unit features) in inductive methods such as BACKPROPAGATION Although PROLOG-EBG does not produce hypotheses that extend the deductive closure of its domain theory, other deductive learning procedures can For example, a domain theory containing determination assertions (eg, "nationality determines language") can be used together with observed data to deductively infer hypotheses that go beyond the deductive closure of the domain theory One important class of problems for which a correct and complete domain theory can be found is the class of large state-space search problems Systems such as PRODIGY SOAR have demonstrated the utility of explanationand based learning methods for automatically acquiring effective search control knowledge that speeds up problem solving in subsequent cases Despite the apparent usefulness of explanation-based learning methods in humans, purely deductive implementations such as PROLOG-EBGsuffer the disadvantage that the output hypothesis is only as correct as the domain theory In the next chapter we examine approaches that combine inductive and analytical learning methods in order to learn effectively from imperfect domain theories and limited training data
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The roots of analytical learning methods can be traced to early work by Fikes et al (1972) on learning macro-operators through analysis of operators in ABSTRIPS and to somewhat later work by Soloway (1977) on the use of explicit prior knowledge in learning Explanation-based learning methods similar to those discussed in this chapter first appeared in a number of systems developed during the early 1980s, including DeJong (1981); Mitchell (1981); Winston et al
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(1983); and Silver (1983) DeJong and Mooney (1986) and Mitchell et al (1986) provided general descriptions of the explanation-based learning paradigm, which helped spur a burst of research on this topic during the late 1980s A collection of research on explanation-based learning performed at the University of Illinois is described by DeJong (1993), including algorithms that modify the structure of the explanation in order to correctly generalize iterative and temporal explanations More recent research has focused on extending explanation-based methods to accommodate imperfect domain theories and to incorporate inductive together with analytical learning (see 12) An edited collection exploring the role of goals and prior knowledge in human and machine learning is provided by Ram and Leake (1995), and a recent overview of explanation-based learning is given by DeJong (1997) The most serious attempts to employ explanation-based learning with perfect domain theories have been in the area of learning search control, or "speedup" learning The SOARsystem described by Laird et al (1986) and the PRODIGY system described by Carbonell et al (1990) are among the most developed systems that use explanation-based learning methods for learning in problem solving Rosenbloom and Laird (1986) discuss the close relationship between SOAR'S learning method (called "chunking") and other explanation-based learning methods More recently, Dietterich and Flann (1995) have explored the combination of explanation-based learning with reinforcement learning methods for learning search control While our primary purpose here is to study machine learning algorithms, it is interesting to note that experimental studies of human learning provide support for the conjecture that human learning is based on explanations For example, Ahn et al (1987) and Qin et al (1992) summarize evidence supporting the conjecture that humans employ explanation-based learning processes Wisniewski and Medin (1995) describe experimental studies of human learning that suggest a rich interplay between prior knowledge and observed data to influence the learning process Kotovsky and Baillargeon (1994) describe experiments that suggest even 11-month old infants build on prior knowledge as they learn The analysis performed in explanation-based learning is similar to certain kinds of program optimization methods used for PROLOG programs, such as partial evaluation; van Harmelen and Bundy (1988) provide one discussion of the relationship
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