Analogy as Nonparametric Bayesian Inference over Relational Systems

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arXiv:2006.04156v2 Announce Type: replace Abstract: Our inferences in the real world are rarely na\"ive - we acquire experiences through our lifetime that can help us more quickly understand the structure of something new. A fundamental question in cognitive science is how we make such generalizations. Studies of analogy have explored the question of how to map information from a single familiar concept or environment to an unfamiliar one. In this paper, we examine how experience with multiple successive environments affects an individual's subsequent inferences. First, we present an online behavioral environment in which participants play a number of virtual games that each operate according to an underlying relational structure. Second, we show that exposing participants to a particular relational structure biases them towards expecting the same structure to hold in the test game, an effect that scales with the number of times the structure has been observed. Finally, we propose a novel probabilistic model that accounts for these behaviors in terms of nonparametric Bayesian inference. This model generates predictions from each past environment based on their relational structures, and then averages predictions from individual environments according to their analogical relevance to the task at hand. Our results and statistical framework provide a complementary perspective for several key computational ideas about analogy, and our nonparametric framework allows us to account for how a learner might continually build and use knowledge over a lifetime.

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