A Diagnostic Tool for Functional Causal Discovery
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函数型因果发现的诊断工具
- 研究问题
- 如何诊断观察性因果发现方法在不同样本量下的方向判断能力，并评估线性、非高斯等假设违反与样本规模的交互影响？
- 方法与思路
- 作者提出 CDDR，将不同子样本量下各类因果发现结果的估计概率绘成曲线，并在双变量情形用于 LiNGAM 和新的检验式方法。
- 材料陈述的贡献
- 摘要称，在一定假设下证明结果概率估计的一致性和渐近正态性，并通过模拟及四个真实数据集展示诊断工具的用途。
- 阅读关注点
- 应核对子样本抽取与概率估计方法、不同诊断结果的定义，以及渐近结论的条件；关注曲线如何区分样本不足与模型假设失效。
- 阅读边界
- 这是 arXiv 预印本，不能据此确认同行评审或期刊接收；摘要未说明具体理论条件，双变量诊断也不能直接推广为多变量因果图的保证。
原文摘要
Causal discovery methods aim to determine the causal direction between variables using observational data. Functional causal discovery methods, such as those based on the Linear Non-Gaussian Acyclic Model (LiNGAM), rely on structural and distributional assumptions to infer the causal direction. However, approaches for assessing causal discovery methods' performance as a function of sample size or the impact of assumption violations, inevitable in real-world scenarios, are lacking. To address this need, we propose Causal Direction Detection Rate (CDDR) diagnostic that evaluates whether and to what extent the interaction between assumption violations and sample size affects the ability to identify the hypothesized causal direction. Given a bivariate dataset of size N on a pair of variables, X and Y, CDDR diagnostic is the plotted comparison of the probability of each causal discovery outcome (e.g. X causes Y, Y causes X, or inconclusive) as a function of sample size less than N. We fully develop CDDR diagnostic in a bivariate case and demonstrate its use for two methods, LiNGAM and our new test-based causal discovery approach. We find CDDR diagnostic for the test-based approach to be more informative since it uses a richer set of causal discovery outcomes. Under certain assumptions, we prove that the probability estimates of detecting each possible causal discovery outcome are consistent and asymptotically normal. Through simulations, we study CDDR diagnostic's behavior when linearity and non-Gaussianity assumptions are violated. Additionally, we illustrate CDDR diagnostic on four real datasets, including three for which the causal direction is known.