Causal discovery has become a vital tool for scientists and practitioners
wanting to discover causal relationships from observational data. While most
previous approaches to causal discovery have implicitly assumed that no expert
domain knowledge is available, practitioners can often provide such domain
knowledge from prior experience. Recent work has incorporated domain knowledge
into constraint-based causal discovery. The majority of such constraint-based
methods, however, assume causal faithfulness, which has been shown to be
frequently violated in practice. Consequently, there has been renewed attention
towards exact-search score-based causal discovery methods, which do not assume
causal faithfulness, such as A*-based methods. However, there has been no
consideration of these methods in the context of domain knowledge. In this
work, we focus on efficiently integrating several types of domain knowledge
into A*-based causal discovery. In doing so, we discuss and explain how domain
knowledge can reduce the graph search space and then provide an analysis of the
potential computational gains. We support these findings with experiments on
synthetic and real data, showing that even small amounts of domain knowledge
can dramatically speed up A*-based causal discovery and improve its performance
and practicality.

本篇论文探讨如何在基于 A * 方法的因果关系发现中高效地整合多种类型的专家领域知识以减少图形搜索空间，并提供了潜在的计算增益分析。作者通过合成数据和真实数据的实验支持这些发现，表明即使少量领域知识都可以极大地提高 A * 方法的效率和实用性。

A * 算法因果发现中的领域知识

Domain Knowledge in A*-Based Causal Discovery

Main approaches for learning Bayesian networks can be classified as
constraint-based, score-based or hybrid methods. Although high-dimensional
consistency results are available for constraint-based methods like the PC
algorithm, such results have not been proved for score-based or hybrid methods,
and most of the hybrid methods have not even shown to be consistent in the
classical setting where the number of variables remains fixed and the sample
size tends to infinity. In this paper, we show that consistency of hybrid
methods based on greedy equivalence search (GES) can be achieved in the
classical setting with adaptive restrictions on the search space that depend on
the current state of the algorithm. Moreover, we prove consistency of GES and
adaptively restricted GES (ARGES) in several sparse high-dimensional settings.
ARGES scales well to sparse graphs with thousands of variables and our
simulation study indicates that both GES and ARGES generally outperform the PC
algorithm.

本文介绍了贝叶斯网络学习的主要方法，包括约束 - based 方法、得分 - based 方法和混合方法。作者提出了一种新的基于贪心等价搜索（GES）的混合方法，并证明了它的一致性。在模拟研究中表明，这种方法相较于 PC 算法，具有更好的性能。

基于得分和混合结构学习的高维一致性

High-dimensional consistency in score-based and hybrid structure  learning

We target the problem of accuracy and robustness in causal inference from
finite data sets. Some state-of-the-art algorithms produce clear output
complete with solid theoretical guarantees but are susceptible to propagating
erroneous decisions, while others are very adept at handling and representing
uncertainty, but need to rely on undesirable assumptions. Our aim is to combine
the inherent robustness of the Bayesian approach with the theoretical strength
and clarity of constraint-based methods. We use a Bayesian score to obtain
probability estimates on the input statements used in a constraint-based
procedure. These are subsequently processed in decreasing order of reliability,
letting more reliable decisions take precedence in case of con icts, until a
single output model is obtained. Tests show that a basic implementation of the
resulting Bayesian Constraint-based Causal Discovery (BCCD) algorithm already
outperforms established procedures such as FCI and Conservative PC. It can also
indicate which causal decisions in the output have high reliability and which
do not.

本论文提出了一种结合贝叶斯方法和约束方法的算法，用于解决从有限数据集进行因果推断的准确性和稳健性问题。