Analogy as Nonparametric Bayesian Inference over Relational Systems

TL;DR

This paper introduces a Bayesian model for relational generalization that leverages analogical reasoning to improve predictions in novel environments, demonstrating a transition from analogy-based to theory-based inference with more experience.

Contribution

The paper presents a novel nonparametric Bayesian framework that formalizes analogy as a method for relational inference and combines it with theory-based learning for improved generalization.

Findings

Outperforms naive learners on relational data with limited experience

Formalizes analogical similarity for selecting and weighting analogies

Shows a transition from analogy-based to theory-based inference as experience increases

Abstract

Much of human learning and inference can be framed within the computational problem of relational generalization. In this project, we propose a Bayesian model that generalizes relational knowledge to novel environments by analogically weighting predictions from previously encountered relational structures. First, we show that this learner outperforms a naive, theory-based learner on relational data derived from random- and Wikipedia-based systems when experience with the environment is small. Next, we show how our formalization of analogical similarity translates to the selection and weighting of analogies. Finally, we combine the analogy- and theory-based learners in a single nonparametric Bayesian model, and show that optimal relational generalization transitions from relying on analogies to building a theory of the novel system with increasing experience in it. Beyond predicting unobserved interactions better than either baseline, this formalization gives a computational-level perspective on the formation and abstraction of analogies themselves.