Domain Recursion for Lifted Inference with Existential Quantifiers

TL;DR

This paper extends the domain recursion inference rule to models with existential quantifiers, showing it can replace Skolemization, avoid negative weights, and reduce inference complexity in relational probability models.

Contribution

It demonstrates that domain recursion can be applied to models with existential quantifiers, providing an alternative to Skolemization and expanding the scope of lifted inference methods.

Findings

Domain recursion can replace Skolemization in models with existential quantifiers.

Applying domain recursion avoids negative weights introduced by Skolemization.

Using domain recursion reduces inference time complexity in example models.

Abstract

In recent work, we proved that the domain recursion inference rule makes domain-lifted inference possible on several relational probability models (RPMs) for which the best known time complexity used to be exponential. We also identified two classes of RPMs for which inference becomes domain lifted when using domain recursion. These two classes subsume the largest lifted classes that were previously known. In this paper, we show that domain recursion can also be applied to models with existential quantifiers. Currently, all lifted inference algorithms assume that existential quantifiers have been removed in pre-processing by Skolemization. We show that besides introducing potentially inconvenient negative weights, Skolemization may increase the time complexity of inference. We give two example models where domain recursion can replace Skolemization, avoids the need for dealing with negative numbers, and reduces the time complexity of inference. These two examples may be interesting from three theoretical aspects: 1- they provide a better and deeper understanding of domain recursion and, in general, (lifted) inference, 2- they may serve as evidence that there are larger classes of models for which domain recursion can satisfyingly replace Skolemization, and 3- they may serve as evidence that better Skolemization techniques exist.