中文摘要：

探索和发现事物间的因果关系是数据科学的一个核心问题,其中蕴含着丰富的科学发现机会和巨大的商业价值.基于非时序观察数据的因果关系发现方法能够从被动观察获得的数据中发现变量之间的因果关系,因而在各领域有广泛应用.这一类方法在过去三十年取得很大进展,已经成为因果关系发现的重要途径.文中从因果关系方向推断、高维数据上的误发现率控制和不完全观察数据上的隐变量检测这三个研究热点出发,对现有的因果关系模型与假设、基于约束的方法、基于因果函数模型的方法和混合型方法这三大类方法,验证与测评涉及的数据集及工具等方面进行了详尽的介绍与分析.基于约束的方法主要包括因果骨架学习和因果方向推断两个阶段：首先基于因果马尔可夫假设,采用条件独立性检验学习变量之间的因果骨架,然后基于奥卡姆剃刀准则利用V-结构确定因果方向,典型的算法有Peter-Clark算法、Inductive Causation等,这类方法的主要不足是存在部分无法判断的因果关系方向,即存在Markov等价类难题.基于因果函数模型的方法则基于数据的因果产生机制假设,在构建变量之间的因果函数模型的基础之上,基于噪声的非高斯性、原因变量与噪声的独立性、原因变量分布与因果函数梯度的独立性等因果假设推断变量之间的因果关系方向,典型的算法有针对线性非高斯无环数据的Linear NonGaussian Acyclic Model算法、针对后非线性数据的Post-NonLinear算法、适用于非线性或离散数据的Additive Noise Model等,这类方法的主要不足是需要较为严格的数据因果机制假设,且Additive Noise Model等方法主要适用于低维数据场景.混合型方法则希望充分发挥基于约束的方法和基于因果函数类方法的优势,分别采用基于约束的方法进行全局结构学习和基于因果函数模型进行局部结构学习和

英文摘要：

Exploring and detecting the causal relations among variables have shown huge practical values in recent years, with numerous opportunities for scientific discovery, and have been commonly seen as the core of data science. Among all possible causal discovery methods, the approaches to causal discovery from non-temporal observational data can recover the causal structures from passive observational data in general cases, and have shown extensive application prospects in a lot of real world applications. After 30 years ＇ rapid progress, causal discovery from non-temporal observational data have been considered as an important research direction of causal discovery. In this survey, we discuss three hot research topics including causal direction inference, false discovery rate control on high-dimensional data, and latent variable detection in partially observational data. Around the above research topics, we extensively review and analyze recent achievements in several aspects of causal discovery, especially focusing on causal models and their basic assumptions, constraint based approaches, casual function based approaches, hybrid approaches, and the related benchmarks and tools. A typical constraint based approach is a two-phase method, firstly utilize the conditional independence tests to learn the causal skeleton based on the Causality Markov Assumption, and then use the V-structures to determine the causal directions based on Occam;s razor principle. The typical constraint based algorithms include Peter-Clark （PC） algorithm and Inductive Causation （IC） algorithm. The main limitation of this class of methods is that they cannot distinguish the underlying causal structure from its statistically equivalent structure, i.e. the algorithms return some undetermined causal directions. This limitation is also known as Markov equivalence class problem. The casual function based approaches are based on data generating process assumptions. After fitting the causal function model among the variables, the causal funct