The discovery of causal relationships from purely observational data is a fundamental problem in science. The most elementary form of such a causal discovery problem is to decide whether X causes Y or, alternatively, Y causes X, given joint observations of two variables X, Y . This was often considered to be impossible. Nevertheless, several approaches for addressing this bivariate causal discovery problem were proposed recently. In this paper, we present the benchmark data set CauseEffectPairs that consists of 88 different "cause-effect pairs" selected from 31 datasets from various domains. We evaluated the performance of several bivariate causal discovery methods on these real-world benchmark data and on artificially simulated data. Our empirical results provide evidence that additive-noise methods are indeed able to distinguish cause from effect using only purely observational data. In addition, we prove consistency of the additive-noise method proposed by Hoyer et al. (2009).

本文回顾了两组单变量因果发现的方法：加性噪声方法（ANM）和信息几何因果推断（IGCI）。作者呈现了一项由各个领域（如，气象学、生物学、医学、工程、经济学等）37个数据集中选择的100个不同因果对的数据基准，这些方法在真实世界基准数据上的实证结果表明，某些方法确实能够仅使用纯观测数据区分原因和效应。

利用观测数据区分因果关系的方法和基准