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Inference in probabilistic logic programs with continuous random variables

机译：具有连续随机变量的概率逻辑程序的推论

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摘要

Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al.'s ProbLog and Vennekens et al.'s LPAD, is aimed at combining statistical and logical knowledge representation and inference. However, the inference techniques used in these works rely on enumerating sets of explanations for a query answer. Consequently, these languages permit very limited use of random variables with continuous distributions. In this paper, we present a symbolic inference procedure that uses constraints and represents sets of explanations without enumeration. This permits us to reason over PLPs with Gaussian or Gamma-distributed random variables (in addition to discrete-valued random variables) and linear equality constraints over reals. We develop the inference procedure in the context of PRISM; however the procedure's core ideas can be easily applied to other PLP languages as well. An interesting aspect of our inference procedure is that PRISM's query evaluation process becomes a special case in the absence of any continuous random variables in the program. The symbolic inference procedure enables us to reason over complex probabilistic models such as Kalman filters and a large subclass of Hybrid Bayesian networks that were hitherto not possible in PLP frameworks.
机译：由Sato和Kameya的PRISM，Poole的ICL，Raedt等人的ProbLog和Vennekens等人的LPAD举例说明的概率逻辑程序设计（PLP）旨在将统计和逻辑知识表示与推理相结合。但是，这些作品中使用的推理技术依赖于枚举查询答案的解释集。因此，这些语言允许非常有限地使用具有连续分布的随机变量。在本文中，我们提出了一种符号推理过程，该过程使用约束并表示无枚举的解释集。这使我们能够对具有高斯或伽马分布随机变量（除了离散值随机变量之外）和实数具有线性等式约束的PLP进行推理。我们在PRISM背景下开发推理程序；但是，该过程的核心思想也可以轻松地应用于其他PLP语言。我们的推理过程的一个有趣的方面是PRISM的查询评估过程在程序中没有任何连续随机变量的情况下成为一种特殊情况。符号推理过程使我们能够推理复杂的概率模型，例如卡尔曼滤波器和混合贝叶斯网络的大型子类，而这些子类在PLP框架中是迄今为止不可能的。

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