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# Analogical Reasoning with Relational Bayesian Sets

*Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics*, PMLR 2:500-507, 2007.

#### Abstract

Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. There are many ways in which objects can be related, making automated analogical reasoning very challenging. Here we develop an approach which, given a set of pairs of related objects S = {A^1:B^1, A^2:B^2, ..., A^N:B^N }, measures how well other pairs A:B fit in with the set S. This addresses the question: is the relation between objects A and B analogous to those relations found in S? We recast this classical problem as a problem of Bayesian analysis of relational data. This problem is nontrivial because direct similarity between objects is not a good way of measuring analogies. For instance, the analogy between an electron around the nucleus of an atom and a planet around the Sun is hardly justified by isolated, non-relational, comparisons of an electron to a planet, and a nucleus to the Sun. We develop a generative model for predicting the existence of relationships and extend the framework of Ghahramani and Heller (2005) to provide a Bayesian measure for how analogous a relation is to other relations. This sheds new light on an old problem, which we motivate and illustrate through practical applications in exploratory data analysis.