Lifted Most Probable Explanation

Abstract

Standard approaches for inference in probabilistic formalisms with first-order constructs include lifted variable elimination (LVE) for single queries, boiling down to computing marginal distributions. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) uses a first-order cluster representation of a knowledge base and LVE in its computations. Another type of query asks for a most probable explanation (MPE) for given events. The purpose of this paper is twofold: (i) We formalise how to compute an MPE in a lifted way with LVE and LJT. (ii) We present a case study in the area of IT security for risk analysis. A lifted computation of MPEs exploits symmetries, while providing a correct and exact result equivalent to one computed on ground level.