Why and How to Learn Why: Analysis-Based Generalization of Procedures

Max Wertheimer, in his classic Productive Thinking, linked understanding to transfer: Understanding is important because it provides the ability to generalize the solution of one problem to apply to another. Recent work in human and machine learning has led to the development of a new class of generalization mechanism, called here analysis-based generalization, which can be used to provide a concrete account of the linkage Wertheimer suggested: these mechanisms all, in different ways, use understanding of examples in the generalization process. In this paper I review this class of mechanism, and describe a method for causal attribution that can produce the analyses of examples that the generalization methods require, in the domain of simple procedures in human-computer interaction. This causal analysis method is linked with analysis-based generalization to form EXPL, an implemented model which is a concrete, though limited, instontiation of Wertheimer s scheme. EXPL constructs an understanding of an example procedure and generalizes it on the basis of that understanding. Results of an empirical study suggest that some of EXPL's attribution heuristics are used by people, and that while a subclass of analysis-based methods, called superstitious methods, seem to provide a more plausible account of people's generalization under the conditions of the study than a contrasting class of rationalistic methods, at least some participants appear to use methods from both classes. The results also show that explanation-based methods, which rely on comprehensive domain theories, must be used in conjunction with a means for extending the domain theory. If thus enhanced, explanation-based methods are able to mimic the effects of other analysis-based methods, and can provide a good account of the data, though combinations of other methods must also be considered. Finally, I return to Wertheimer s ideas to argue that none of the current analysis-based generalization methods fully captures Wertheimer s notion of understanding. Proper choice among different possible analyses of an example is crucial for Wertheimer, but I argue that this problem may be beyond the reach of learning systems.