| Summary: | In recent years, the Markov Logic Network (MLN) has emerged as a powerful tool for knowledge-based inference due to its ability to combine first-order logic inference and probabilistic reasoning. Unfortunately, current MLN solutions cannot efficiently support knowledge inference involving arithmetic expressions, which is required to model the interaction between logic relations and numerical values in many real applications. In this paper, we propose a probabilistic inference framework, called the Numerical Markov Logic Network (NMLN), to enable efficient inference of hybrid knowledge involving both logic and arithmetic expressions. We first introduce the hybrid knowledge rules, then define an inference model, and finally, present a technique based on convex optimization for efficient inference. Built on decomposable exp-loss function, the proposed inference model can process hybrid knowledge rules more effectively and efficiently than the existing MLN approaches. Finally, we empirically evaluate the performance of the proposed approach on real data. Our experiments show that compared to the state-of-the-art MLN solution, it can achieve better prediction accuracy while significantly reducing inference time.
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