New Liftable Classes for First-Order Probabilistic Inference

TL;DR

This paper demonstrates that the domain recursion inference rule significantly enhances the power of lifted inference in probabilistic relational models, enabling polynomial-time inference for a broader class of models previously thought intractable.

Contribution

It reveals the increased power of domain recursion in lifted inference, extending the range of models with polynomial-time inference and introducing new classes of domain-liftable theories.

Findings

Domain recursion extends polynomial-time inference to new models.

S4, the symmetric transitivity model, is shown to be domain-liftable.

Exponential speedup achieved in theories not fully liftable with existing rules.

Abstract

Statistical relational models provide compact encodings of probabilistic dependencies in relational domains, but result in highly intractable graphical models. The goal of lifted inference is to carry out probabilistic inference without needing to reason about each individual separately, by instead treating exchangeable, undistinguished objects as a whole. In this paper, we study the domain recursion inference rule, which, despite its central role in early theoretical results on domain-lifted inference, has later been believed redundant. We show that this rule is more powerful than expected, and in fact significantly extends the range of models for which lifted inference runs in time polynomial in the number of individuals in the domain. This includes an open problem called S4, the symmetric transitivity model, and a first-order logic encoding of the birthday paradox. We further identify new classes S2FO2 and S2RU of domain-liftable theories, which respectively subsume FO2 and recursively unary theories, the largest classes of domain-liftable theories known so far, and show that using domain recursion can achieve exponential speedup even in theories that cannot fully be lifted with the existing set of inference rules.