Synthetic datasets generated by structural causal models (SCMs) are commonly used for benchmarking causal structure learning algorithms. However, the variances and pairwise correlations in SCM data tend to increase along the causal ordering. Several popular algorithms exploit these artifacts, possibly leading to conclusions that do not generalize to real-world settings. Existing metrics like $\operatorname{Var}$-sortability and $\operatorname{R^2}$-sortability quantify these patterns, but they do not provide tools to remedy them. To address this, we propose internally-standardized structural causal models (iSCMs), a modification of SCMs that introduces a standardization operation at each variable during the generative process. By construction, iSCMs are not $\operatorname{Var}$-sortable, and as we show experimentally, not $\operatorname{R^2}$-sortable either for commonly-used graph families. Moreover, contrary to the post-hoc standardization of data generated by standard SCMs, we prove that linear iSCMs are less identifiable from prior knowledge on the weights and do not collapse to deterministic relationships in large systems, which may make iSCMs a useful model in causal inference beyond the benchmarking problem studied here.

翻译：结构因果模型（SCMs）生成的合成数据集通常用于基准测试因果结构学习算法。然而，SCM数据中的方差和成对相关性往往沿着因果顺序增加。若干流行算法利用了这些人为特征，可能导致结论无法推广到真实世界场景。现有指标如$\operatorname{Var}$-可排序性与$\operatorname{R^2}$-可排序性能量化这些模式，但未提供修正工具。为此，我们提出内部标准化结构因果模型（iSCMs），通过在生成过程中对每个变量引入标准化操作来改进SCMs。从构造上，iSCMs不具有$\operatorname{Var}$-可排序性，且实验表明对于常用图族也不具有$\operatorname{R^2}$-可排序性。此外，与标准SCMs生成数据的后验标准化相反，我们证明线性iSCMs通过权重先验知识的可识别性更低，且不会在大规模系统中退化为确定性关系，这可能使iSCMs成为超越本文研究的基准测试问题的因果推断中有用的模型。