Enabling Causal Discovery in Post-Nonlinear Models with Normalizing Flows

TL;DR

This paper introduces CAF-PoNo, a novel method using normalizing flows to enforce invertibility in post-nonlinear causal models, improving causal discovery accuracy in complex settings.

Contribution

The paper presents a new normalizing flows-based approach for PNL models that accurately enforces invertibility and extends to multivariate causal discovery.

Findings

Outperforms state-of-the-art methods in simulated data

Effective in real-world causal discovery tasks

Handles complex multivariate causal relationships

Abstract

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.