Post-nonlinear (PNL) causal models stand out as a versatile and adaptable framework for modeling intricate causal relationships. However, accurately capturing the invertibility constraint required in PNL models remains challenging in existing studies. To address this problem, we introduce CAF-PoNo (Causal discovery via Normalizing Flows for Post-Nonlinear models), harnessing the power of the normalizing flows architecture to enforce the crucial invertibility constraint in PNL models. Through normalizing flows, our method precisely reconstructs the hidden noise, which plays a vital role in cause-effect identification through statistical independence testing. Furthermore, the proposed approach exhibits remarkable extensibility, as it can be seamlessly expanded to facilitate multivariate causal discovery via causal order identification, empowering us to efficiently unravel complex causal relationships. Extensive experimental evaluations on both simulated and real datasets consistently demonstrate that the proposed method outperforms several state-of-the-art approaches in both bivariate and multivariate causal discovery tasks.

翻译：后非线性（PNL）因果模型作为一种通用且适应性强的框架，在建模复杂因果关系方面表现突出。然而，现有研究仍难以准确满足PNL模型所要求的可逆性约束。为解决此问题，我们提出了CAF-PoNo（基于归一化流的后非线性模型因果发现方法），利用归一化流架构的强大能力来强制实施PNL模型中的关键可逆性约束。通过归一化流，我们的方法能精确重构隐藏噪声，这在通过统计独立性检验进行因果识别中起着至关重要的作用。此外，所提方法展现出卓越的可扩展性，可通过因果序识别无缝扩展至多变量因果发现，使我们能够有效揭示复杂因果关系。在模拟和真实数据集上进行的大量实验评估一致表明，所提方法在双变量和多变量因果发现任务中均优于多种现有先进方法。