2017/07/24 by Seyed Mehran Kazemi, Kazemi, Seyed Mehran, Angelika Kimmig +5 · 2 citations
Computer Science · #AI-based Problem Solving and Planning #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Machine Learning and Algorithms
paper · pdf · doi:10.48550/arxiv.1707.07763
openalex publication_date 2017/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.