A Kernel Embedding-based Approach for Nonstationary Causal Model Inference

TL;DR

This paper introduces ENCI, a kernel embedding-based method for inferring causal directions and graphs from nonstationary data collected across multiple domains, leveraging distributional changes for improved identifiability.

Contribution

ENCI is a novel approach that transforms cause-effect relations into linear models of kernel embeddings, enabling causal inference in nonstationary settings, including causal graph discovery.

Findings

ENCI accurately infers causal directions in synthetic and real-world data.

It extends to causal graph discovery under mild conditions.

Outperforms existing methods in nonstationary scenarios.

Abstract

Although nonstationary data are more common in the real world, most existing causal discovery methods do not take nonstationarity into consideration. In this letter, we propose a kernel embedding-based approach, ENCI, for nonstationary causal model inference where data are collected from multiple domains with varying distributions. In ENCI, we transform the complicated relation of a cause-effect pair into a linear model of variables of which observations correspond to the kernel embeddings of the cause-and-effect distributions in different domains. In this way, we are able to estimate the causal direction by exploiting the causal asymmetry of the transformed linear model. Furthermore, we extend ENCI to causal graph discovery for multiple variables by transforming the relations among them into a linear nongaussian acyclic model. We show that by exploiting the nonstationarity of distributions, both cause-effect pairs and two kinds of causal graphs are identifiable under mild conditions. Experiments on synthetic and real-world data are conducted to justify the efficacy of ENCI over major existing methods.