In many probabilistic first-order representation systems, inference is
performed by "grounding"---i.e., mapping it to a propositional representation,
and then performing propositional inference. With a large database of facts,
groundings can be very large, making inference and learning computationally
expensive. Here we present a first-order probabilistic language which is
well-suited to approximate "local" grounding: every query $Q$ can be
approximately grounded with a small graph. The language is an extension of
stochastic logic programs where inference is performed by a variant of
personalized PageRank. Experimentally, we show that the approach performs well
without weight learning on an entity resolution task; that supervised
weight-learning improves accuracy; and that grounding time is independent of DB
size. We also show that order-of-magnitude speedups are possible by
parallelizing learning.

本文提出了一种适合近似局部接地的一阶概率语言，在实验中通过权值学习得出更高的准确性，并且与数据库大小无关的接地时间以及将学习并行化可实现数量级的加速。

个性化 PageRank 编程：一种局部可归类一阶概率逻辑

Programming with Personalized PageRank: A Locally Groundable First-Order  Probabilistic Logic

Recent work on loglinear models in probabilistic constraint logic programming
is applied to first-order probabilistic reasoning. Probabilities are defined
directly on the proofs of atomic formulae, and by marginalisation on the atomic
formulae themselves. We use Stochastic Logic Programs (SLPs) composed of
labelled and unlabelled definite clauses to define the proof probabilities. We
have a conservative extension of first-order reasoning, so that, for example,
there is a one-one mapping between logical and random variables. We show how,
in this framework, Inductive Logic Programming (ILP) can be used to induce the
features of a loglinear model from data. We also compare the presented
framework with other approaches to first-order probabilistic reasoning.

该论文探讨了在概率约束逻辑编程中对数线性模型的研究，并将其应用到一阶概率推理中，介绍了基于标记和未标记的确定性子句确定证明概率的随机逻辑程序概率定义，通过归一化证明概率中原子公式本身的概率，扩展了相关理论，同时通过归纳逻辑编程从数据中归纳出对数线性模型的特征，最后用其他方法对其进行比较。

一阶概率推理的对数线性模型

Loglinear models for first-order probabilistic reasoning

Algorithms for exact and approximate inference in stochastic logic programs
(SLPs) are presented, based respectively, on variable elimination and
importance sampling. We then show how SLPs can be used to represent prior
distributions for machine learning, using (i) logic programs and (ii) Bayes net
structures as examples. Drawing on existing work in statistics, we apply the
Metropolis-Hasting algorithm to construct a Markov chain which samples from the
posterior distribution. A Prolog implementation for this is described. We also
discuss the possibility of constructing explicit representations of the
posterior.

本研究介绍了基于变量消除和重要性采样的精确和近似概率推理算法，并展示了如何使用 SLPs 股票机器学习的先验分布，包括逻辑程序和贝叶斯网结构。作者还应用 Metropolis-Hasting 算法，构建了一个从后验分布中采样的马尔科夫链，同时讨论了构建后验明确表示的可能性。