Bivariate Causal Discovery via Conditional Divergence

Bao Duong, Thin Nguyen

Keywords: causal discovery, causal direction, conditional divergence

TL;DR: We propose a novel method for predicting the causal direction between two univariate variables, by measuring the stability of the conditional distributions of the effect given the cause.

Abstract: Telling apart cause and effect is a fundamental problem across many science disciplines. However, the randomized controlled trial, which is the golden-standard solution for this, is not always physically feasible or ethical. Therefore, we can only rely on passively observational data in such cases, making the problem highly challenging. Inspired by the observation that the conditional distribution of effect given cause, also known as the causal mechanism, is typically invariant in shape, we aim to capture the mechanism through estimating the stability of the conditional distribution. In particular, based on the inverse of stability – the divergence – we propose Conditional Divergence based Causal Inference (CDCI), a novel algorithm for detecting causal direction in purely observational data. By doing this, we can relax multiple strict assumptions commonly adopted in the causal discovery literature, including functional form and noise model. The proposed approach is generic and applicable to arbitrary measures of distribution divergence. The effectiveness of our method is demonstrated on a variety of both synthetic and real data sets, which compares favorably with existing state-of-the-art methods.