Fusing First-order Knowledge Compilation and the Lifted Junction Tree Algorithm

TL;DR

This paper proposes a framework that integrates first-order knowledge compilation with the lifted junction tree algorithm, enabling more efficient probabilistic inference by leveraging the strengths of both methods.

Contribution

It introduces a method to use any exact inference algorithm as a subroutine within the lifted junction tree framework, improving inference efficiency for certain inputs.

Findings

FOKC integrated into LJT accelerates inference for specific cases.

The approach outperforms standalone LVE, LJT, and FOKC in speed for some models.

The framework enhances the flexibility and efficiency of lifted probabilistic inference.

Abstract

Standard approaches for inference in probabilistic formalisms with first-order constructs include lifted variable elimination (LVE) for single queries as well as first-order knowledge compilation (FOKC) based on weighted model counting. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) uses a first-order cluster representation of a model and LVE as a subroutine in its computations. For certain inputs, the implementations of LVE and, as a result, LJT ground parts of a model where FOKC has a lifted run. The purpose of this paper is to prepare LJT as a backbone for lifted inference and to use any exact inference algorithm as subroutine. Using FOKC in LJT allows us to compute answers faster than LJT, LVE, and FOKC for certain inputs.