Complex Markov Logic Networks: Expressivity and Liftability
This addresses a theoretical bottleneck in probabilistic relational models for AI researchers, offering a more efficient method for inference tasks.
The paper tackles the expressivity limitation of standard Markov logic networks (MLNs) by introducing complex MLNs with complex-valued weights, proving they are fully expressive, and uses this to design an algorithm for computing relational marginal polytopes that requires substantially fewer calls to a WFOMC oracle.
We study expressivity of Markov logic networks (MLNs). We introduce complex MLNs, which use complex-valued weights, and we show that, unlike standard MLNs with real-valued weights, complex MLNs are fully expressive. We then observe that discrete Fourier transform can be computed using weighted first order model counting (WFOMC) with complex weights and use this observation to design an algorithm for computing relational marginal polytopes which needs substantially less calls to a WFOMC oracle than a recent algorithm.