Structure learning is a core problem in AI central to the fields of
neuro-symbolic AI and statistical relational learning. It consists in
automatically learning a logical theory from data. The basis for structure
learning is mining repeating patterns in the data, known as structural motifs.
Finding these patterns reduces the exponential search space and therefore
guides the learning of formulas. Despite the importance of motif learning, it
is still not well understood. We present the first principled approach for
mining structural motifs in lifted graphical models, languages that blend
first-order logic with probabilistic models, which uses a stochastic process to
measure the similarity of entities in the data. Our first contribution is an
algorithm, which depends on two intuitive hyperparameters: one controlling the
uncertainty in the entity similarity measure, and one controlling the softness
of the resulting rules. Our second contribution is a preprocessing step where
we perform hierarchical clustering on the data to reduce the search space to
the most relevant data. Our third contribution is to introduce an O(n ln n) (in
the size of the entities in the data) algorithm for clustering
structurally-related data. We evaluate our approach using standard benchmarks
and show that we outperform state-of-the-art structure learning approaches by
up to 6% in terms of accuracy and up to 80% in terms of runtime.

本文提出了一种基于随机过程的方法来挖掘抽象化的图形模型中的结构语素，并通过标准测试发现其准确度比现有的结构学习方法高出了 6％，计算时间快 80％.

基于结构学习的正义高效 Motif 搜索算法

Principled and Efficient Motif Finding for Structure Learning of Lifted Graphical Models

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。