FIGCI: Flow-Based Information-Geometric Causal Inference

Shengyuan Zhang, Jingyu Wu, Zejian Li, Li Liu, Jun Liao, Lingyun Sun

Abstract: This paper is concerned with causal discovery between two random variables X and Y with observational data. Information-Geometric Causal Inference (IGCI) is a well-established method to identify the causal direction between two variables. It assumes the cause distribution and causal mechanism are independent. However, IGCI requires the causal mechanism to be a diffeomorphism function. Fortunately, flow-based models are designed to be differentiable and have a differentiable inverse with a large capacity. We propose Flow-based IGCI (FIGCI). First, the flow-based model fits an invertible mapping between X and Y with two proposed training strategies. Second, FIGCI predicts the causal direction according to the estimated covariances between X as well as Y and the invertible mapping. Empirical studies exemplify the efficacy of FIGCI.