Statistical relational models provide compact encodings of probabilistic
dependencies in relational domains, but result in highly intractable graphical
models. The goal of lifted inference is to carry out probabilistic inference
without needing to reason about each individual separately, by instead treating
exchangeable, undistinguished objects as a whole. In this paper, we study the
domain recursion inference rule, which, despite its central role in early
theoretical results on domain-lifted inference, has later been believed
redundant. We show that this rule is more powerful than expected, and in fact
significantly extends the range of models for which lifted inference runs in
time polynomial in the number of individuals in the domain. This includes an
open problem called S4, the symmetric transitivity model, and a first-order
logic encoding of the birthday paradox. We further identify new classes S2FO2
and S2RU of domain-liftable theories, which respectively subsume FO2 and
recursively unary theories, the largest classes of domain-liftable theories
known so far, and show that using domain recursion can achieve exponential
speedup even in theories that cannot fully be lifted with the existing set of
inference rules.

在这篇论文中，我们研究了域递推推理规则，它被认为是冗余的。我们发现，这个规则比预期的更强大，并且实际上显著扩展了模型的范围，其中一些模型的抬升推理时间多项式增长。我们还确定了新的域可抬升理论类别，其中一些理论的使用域递推可以实现指数加速。

一阶概率推断的新可提升类别

New Liftable Classes for First-Order Probabilistic Inference

This article presents a survey of work on lifted graphical models. We review
a general form for a lifted graphical model, a par-factor graph, and show how a
number of existing statistical relational representations map to this
formalism. We discuss inference algorithms, including lifted inference
algorithms, that efficiently compute the answers to probabilistic queries. We
also review work in learning lifted graphical models from data. It is our
belief that the need for statistical relational models (whether it goes by that
name or another) will grow in the coming decades, as we are inundated with data
which is a mix of structured and unstructured, with entities and relations
extracted in a noisy manner from text, and with the need to reason effectively
with this data. We hope that this synthesis of ideas from many different
research groups will provide an accessible starting point for new researchers
in this expanding field.

该文章综述了关于提升图模型的工作。它介绍了提升图模型的一般形式，即 par - 因子图，并展示了许多现有的统计关系表达式如何映射到这种形式。文章讨论了包括提升推断算法在内的推理算法，它们可以高效地计算概率查询的答案。此外，文章还回顾了从数据中学习提升图模型的研究工作。我们相信在未来数十年中，对于统计关系模型（不管叫什么名字）的需求将会增加，因为我们将面对各种结构化和非结构化数据的混合，这些数据以一种嘈杂的方式从文本中提取出实体和关系，并且需要有效地处理这些数据。我们希望这篇综述可以为这个扩展领域的新研究者提供一个可访问的起点。