Enabling Causal Discovery in Post-Nonlinear Models with Normalizing Flows
This work addresses a specific bottleneck in causal discovery for researchers, offering an incremental improvement by applying normalizing flows to enhance existing post-nonlinear models.
The paper tackles the challenge of accurately capturing the invertibility constraint in post-nonlinear causal models by introducing CAF-PoNo, which uses normalizing flows to enforce this constraint and reconstruct hidden noise for cause-effect identification, resulting in outperformance of state-of-the-art methods in bivariate and multivariate causal discovery tasks.
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.