Recent progress in Neural Causal Models (NCMs) showcased how identification and partial identification of causal effects can be automatically carried out via training of neural generative models that respect the constraints encoded in a given causal graph [Xia et al. 2022, Balazadeh et al. 2022]. However, formal consistency of these methods has only been proven for the case of discrete variables or only for linear causal models. In this work, we prove consistency of partial identification via NCMs in a general setting with both continuous and categorical variables. Further, our results highlight the impact of the design of the underlying neural network architecture in terms of depth and connectivity as well as the importance of applying Lipschitz regularization in the training phase. In particular, we provide a counterexample showing that without Lipschitz regularization the NCM may not be asymptotically consistent. Our results are enabled by new results on the approximability of structural causal models via neural generative models, together with an analysis of the sample complexity of the resulting architectures and how that translates into an error in the constrained optimization problem that defines the partial identification bounds.

翻译：近年来，神经因果模型（NCMs）的研究进展展示了如何通过训练符合给定因果图所编码约束的神经生成模型，来自动实现因果效应的识别与部分识别 [Xia et al. 2022, Balazadeh et al. 2022]。然而，这些方法的正式可一致性仅在离散变量情形或仅在线性因果模型中得到证明。在本工作中，我们证明了在包含连续变量与分类变量的一般设定下，通过NCMs进行部分识别的可一致性。此外，我们的结果强调了底层神经网络架构在深度与连接性方面的设计影响，以及在训练阶段应用Lipschitz正则化的重要性。特别地，我们提供了一个反例，表明若无Lipschitz正则化，NCM可能不具备渐近一致性。我们的结论得益于关于结构因果模型通过神经生成模型可逼近性的新结果，并结合了对所得架构样本复杂度的分析，以及该复杂度如何转化为定义部分识别边界的约束优化问题中的误差。