Variation-based Cause Effect Identification

TL;DR

This paper introduces VCEI, a novel variation-based framework for causal discovery in bivariate systems that leverages distribution variations and kernel methods to identify cause-effect relationships from observational data.

Contribution

The paper presents a new variation-based causal discovery method that uses artificial distribution shifts and kernel maximum mean discrepancy to determine causal direction.

Findings

VCEI effectively identifies causal directions in real and synthetic data.

The framework is flexible across different data types due to kernel-based formulation.

VCEI is competitive with existing cause-effect identification methods.

Abstract

Mining genuine mechanisms underlying the complex data generation process in real-world systems is a fundamental step in promoting interpretability of, and thus trust in, data-driven models. Therefore, we propose a variation-based cause effect identification (VCEI) framework for causal discovery in bivariate systems from a single observational setting. Our framework relies on the principle of independence of cause and mechanism (ICM) under the assumption of an existing acyclic causal link, and offers a practical realization of this principle. Principally, we artificially construct two settings in which the marginal distributions of one covariate, claimed to be the cause, are guaranteed to have non-negligible variations. This is achieved by re-weighting samples of the marginal so that the resultant distribution is notably distinct from this marginal according to some discrepancy measure. In the causal direction, such variations are expected to have no impact on the effect generation mechanism. Therefore, quantifying the impact of these variations on the conditionals reveals the genuine causal direction. Moreover, we formulate our approach in the kernel-based maximum mean discrepancy, lifting all constraints on the data types of cause-and-effect covariates, and rendering such artificial interventions a convex optimization problem. We provide a series of experiments on real and synthetic data showing that VCEI is, in principle, competitive to other cause effect identification frameworks.