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Analogy as Nonparametric Bayesian Inference over Relational Systems
Abstract
Much of human learning and inference can be framed withinthe computational problem of relational generalization. Inthis project, we propose a Bayesian model that generalizesrelational knowledge to novel environments by analogicallyweighting predictions from previously encountered relationalstructures. First, we show that this learner outperforms anaive, theory-based learner on relational data derived fromrandom- and Wikipedia-based systems when experience withthe environment is small. Next, we show how our formal-ization of analogical similarity translates to the selection andweighting of analogies. Finally, we combine the analogy-and theory-based learners in a single nonparametric Bayesianmodel, and show that optimal relational generalizationtransitions from relying on analogies to building a theory ofthe novel system with increasing experience in it. Beyondpredicting unobserved interactions better than either baseline,this formalization gives a computational-level perspective onthe formation and abstraction of analogies themselves.
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