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Explanation-Based Generalization: a Unifying View

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Explanation-Based Generalization: a Unifying View Machine Learning 1: 47-80, 1986 © 1986 Kluwer Academic Publishers, Boston - Manufactured in The Netherlands Explanation-Based Generalization: A Unifying View TOM M. MITCHELL (MITCHELL @ RED.RUTGERS.EDU) RICHARD M. KELLER (KELLER @ RED.RUTGERS.EDU) SMADAR T. KEDAR-CABELLI (KEDAR-CABELLI @ RED.RUTGERS.EDU) Computer Science Department, Rutgers University, New Brunswick, NJ 08903, U.S.A. (Received August 1, 1985) Key words: explanation-basedlearning, explanation-based generalization, goal regression, constraint back-propagation, operationalization,similarity-based generalization. Abstract. The problem of formulating general concepts from specific training examples has long been a major focus of machine learning research. While most previous research has focused on empirical methods for generalizing from a large number of training examples using no domain-specific knowledge, in the past few years new methods have been developedfor applying domain-specific knowledge to for- mulate valid generalizations from single training examples. The characteristic common to these methods is that theirability to generalize from asingle example followsfrom theirability toexplainwhy the training example is a member of the concept being learned. This paper proposes a general, domain-independent mechanism, called that unifiesprevious approachesto explanation-basedgeneralization. The EBG method is illustrated in the context of several exampleproblems, and used to contrast several existing systems for explanation-basedgeneralization. The perspective on explanation-basedgeneralization af- forded by this general method is also used to identify open research problems in this area. 1. Introduction and motivation The abilityto generalize from examplesis widely recognized as an essential capability of any learning system. Generalization involves observing a set of training examples of some general conceptT^eiitTfyTri'glhF features common to these ex- amples, then formulating a concept definition based on these common features. The generalizatktnprpcesscan thus be viewed as a search through a vast space of possible concept defirTitionTfin search ofa correct definition of the concept to be learned. Because this space ofpossible concept definitions is vast, the heart ot the generaliza- tion problem lies in utilizingwhatever trainingdata, assumptionsjinjijmo^ available to constrain this search. "^olFrVsea^ generalization problem has focused on empirical, data- intensive methods that rely on large numbers of training examples to constrain the search for the correct generalization(see Mitchell, 1982; Michalski, 1983; Dietterich, EBG, 48 T.M. MITCHELL, R.M. KELLER AND S.T. KEDAR-CABELLI 1982 for overviews of these methods).These methods all employ somekind of induc- tive bias to guide the inductive leapthat they must make in orderto define a concept I from only a subset of its examples(Mitchell, 1980). This bias is typically built into the generalizer by providing it with knowledge onlyof those example features that are presumed relevant to describing the concept to be learned. Through various algorithms it is then possible to search through the restricted space of concepts definable in terms of these allowed features, to determine concept definitions consis- tent with the training examples. Because these methods are based on searching for features that are common to the training examples, we shall refer to them as similarity-basedgeneralizationmethods. 1 In recent years, a number of researchers have proposed generalizationmethods that contrast sharply with these data-intensive, similarity-based methods (e.g., Borgida et al., 1985; DeJong, 1983; Kedar-Cabelli, 1985; Keller, 1983; Lebowitz, 1985; Mahadevan, 1985; Minton, 1984; Mitchell, 1983; Mitchell et al., 1985; O'Rorke, 1984; Salzberg & Atkinson, 1984; Schank, 1982; Silver, 1983; Utgoff, 1983; Winston et al., 1983). Rather than relying on many training examplesand an inductive bias to constrain the search for a correct generalization, these more recent methods constrain the search by relying on knowledgeof the task domain and of the concept under study. After analyzing a single training example, in terms of this knowledge, these methods are able to produce a valid generalizationof the example along with a deductive justificationof the generalization in terms of the system's klwwleT}g"eTMo'rVpTecisdy, these exptanaTiori-based methods2 analyze the training exampleby first constructing an explanationof how the examplesatisfies the defini- tion of the concept under study. The features of the exampleidentified by this ex- planation are then used as the basis for formulating the generalconcept definition. The justificationfor this concept definition follows from theexplanation constructed for the training example. Thus, by relying on knowledge of the domain and of the concept under study, explanation-basedmethods overcome the fundamental difficulty associated with in- ductive, similarity-based methods: their inability to justifythe generalizationsthat they produce. The basic difference between the two classes of methods is that similarity-based methods must rely on some form of inductive bias to guide generalization,whereas explanation-based methods rely instead on their domain knowledge. While explanation-based methods provide a more reliable means of 1 The term similarity-based generalization was suggested by Lebowitz (1985). We use this term to cover both methods that search for similarities among positiveexamples, and for differences between positive and negative examples. SJ-j 2 The term explanation-basedgeneralization was first introduced by DeJong (1981) to describe his par- '_> ticular generalization method. The authors have previously used the term goal-directed generalization (Mitchell, 1983) to refer to their own explanation-basedgeneralization method. In this paper, we use the term explanation-basedgeneralization to refer to the entire class of methods that formulate generaliza- tions by constructing explanations. EXPLANATION-BASED GENERALIZATION 49 generalization,and are able to extract more information from individual training examples, they also require that the learner possess knowledgeof the domain and of the concept under study. It seems clear that for a large number of generalization problems encountered by intelligent agents, this required knowledge is available to the learner. In this paper we present and analyze a number of such generalization problems. The purpose of this paper is to consider in detail the capabilitiesand requirements of explanation-based approaches to generalization, and to introduce a single mechanism that unifies previously described approaches. In particular, we present a domain-independent method (calledEBG) for utilizing domain-specificknowledge to guide generalization, and illustrate its use in a numberof generalizationtasks that have previously been approached using differing explanation-basedmethods. EBG constitutes a more general mechanism for explanation-basedgeneralization than these previous approaches. Because it requires a larger numberofexplicit inputs(i.e., the trainingexample,a domain theory, a definition of the concept under study, and a description of the form in which the learned concept must be expressed) EBG can be instantiated for a wider varietyof learning tasks. Finally, EBG provides a perspec- tive for identifying the present limitations of explanation-basedgeneralization, and for identifying open research problems in this area. The remainder of this paper is organized as follows. Section 2 introduces the general EBG method for explanation-based generalization, and illustrates the method with an example. Section 3 then illustrates the EBG method in the context oftwo additional examples: (1) learning a structural definition ofa cup from a train- ing exampleplus knowledge about the function of a cup (based on Winston et al.'s (1983) work), and (2) learning a search heuristic from an example search tree plus knowledge about search and the search space (based on Mitchell et al.'s (1983) work on the LEX system). Section 4 concludes with a generalperspective on explanation- based generalizationand a discussion of significant open research issues in this area. The appendix relates DeJong's (1981, 1983) research on explanation-based generalizationand explanatoryschema acquisition to the other work discussed here. 2. Explanation-basedgeneralization: discussion and an example Thekey insight behind explanation-basedgeneralizationis that it is possible to form a justifiedgeneralizationof a single positive training exampleprovidedthe learning system is endowed with some explanatory capabilities.Inparticular, the system must be able to explainto itself why the training example is an example of the concept under study. Thus, the generalizeris presumed to possess a definition of the concept under study as well as domain knowledge for constructing therequired explanation. In this section, we define more precisely the class of generalizationproblemscovered by explanation-basedmethods, define the generalEBG method, and illustrate it in terms of a specific example problem. 50 T.M. MITCHELL, R.M. KELLER AND S.T. KEDAR-CABELLI 2. 1 The explanation-basedgeneralizationproblem In order to define the generalization problem considered here, we first introduce some terminology. A concept is defined as a predicate over some universe of in- stances, and thus characterizes some subset of the instances. Each instance in this universe is describedby a collection of groundliterals
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