Nonparametric Bayesian Logic

TL;DR

This paper extends Bayesian Logic (BLOG) with nonparametric methods, enabling flexible modeling of unknown object collections and attributes, demonstrated through citation matching applications.

Contribution

It introduces nonparametric generative processes into BLOG, allowing for reasoning about arbitrary object collections and improving inference over varying object numbers.

Findings

Uses Dirichlet processes for modeling unknown objects.

Provides an intuitive syntax for reasoning about object collections.

Demonstrates effectiveness in citation matching.

Abstract

The Bayesian Logic (BLOG) language was recently developed for defining first-order probability models over worlds with unknown numbers of objects. It handles important problems in AI, including data association and population estimation. This paper extends BLOG by adopting generative processes over function spaces - known as nonparametrics in the Bayesian literature. We introduce syntax for reasoning about arbitrary collections of objects, and their properties, in an intuitive manner. By exploiting exchangeability, distributions over unknown objects and their attributes are cast as Dirichlet processes, which resolve difficulties in model selection and inference caused by varying numbers of objects. We demonstrate these concepts with application to citation matching.