通过剔除变量验证因果发现模型,无需真实因果关系即可评估其准确性。
Cross-validating causal discovery via Leave-One-Variable-Out
- 用剔除单个变量的数据集训练模型,再推断被剔变量间的关系。
- 在无联合观测数据时仍能预测条件期望,误差可估且与模型准确率相关。
- 适用于各类因果算法,尤其适合有先验假设的线性模型,可作模型可信度检验。
我们提出一种无需真实因果关系即可验证因果发现算法的新方法,基于在学习过程中剔除某一变量后,对剩余变量对进行因果建模。给定变量组 $X, Y, \boldsymbol{Z}=X, Y, Z_1,\dots,Z_k$,分别在剔除 $Y$ 得到的 $X, \boldsymbol{Z}$ 与剔除 $X$ 得到的 $Y, \boldsymbol{Z}$ 数据集上运行因果发现算法,得到两类因果模型(如 DAG、ADMG、CPDAG、PAG)。这些模型常能推导出 $X$ 与 $Y$ 之间的依赖关系,并可在仅知剔除后数据的前提下估计 $\mathbb{E}(Y\mid X=x)$,该过程称为“留一变量外(LOVO)”预测。由于联合分布 $P(X, Y)$ 可得,且 $X$ 与 $Y$ 仅被用于剔除验证,因此可估计预测误差。我们提出两种 LOVO 预测变体:一种通用图形方法,适用于任意因果发现算法;另一种针对特定先验假设(如线性加性噪声模型)的算法。模拟实验表明,LOVO 预测误差与因果输出准确率显著相关,证实了该方法的有效性。
原文摘要 · Abstract (English)
We propose a new approach to falsify causal discovery algorithms without ground truth, which is based on testing the causal model on a variable pair excluded during learning the causal model. Specifically, given data on $X, Y, \boldsymbol{Z}=X, Y, Z_1,\dots,Z_k$, we apply the causal discovery algorithm separately to the 'leave-one-out' data sets $X, \boldsymbol{Z}$ and $Y, \boldsymbol{Z}$. We demonstrate that the two resulting causal models, in the form DAGs, ADMGs, CPDAGs or PAGs, often entail conclusions on the dependencies between $X$ and $Y$ and allow to estimate $\mathbb{E}(Y\mid X=x)$ without any joint observations of $X$ and $Y$, given only the leave-one-out datasets. This estimation is called "Leave-One-Variable-Out (LOVO)" prediction. Its error can be estimated since the joint distribution $P(X, Y)$ is available, and $X$ and $Y$ have only been omitted for the purpose of falsification. We present two variants of LOVO prediction: One graphical method, which is applicable to general causal discovery algorithms, and one version tailored towards algorithms relying on specific a priori assumptions, such as linear additive noise models. Simulations indicate that the LOVO prediction error is indeed correlated with the accuracy of the causal outputs, affirming the method's effectiveness.
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