Distinguishing Cause from Effect with Causal Velocity Models

TL;DR

This paper introduces a novel causal discovery method using velocity models and score functions, enabling causal inference without strict noise assumptions, and demonstrates its effectiveness in simulations and benchmarks.

Contribution

It proposes a new velocity-based parametrization of SCMs and a regression approach to causal discovery that surpasses existing methods in flexibility and robustness.

Findings

Effective in simulation and benchmark tests

Handles complex noise distributions without assumptions

Detects model non-identifiability and misspecification

Abstract

Bivariate structural causal models (SCM) are often used to infer causal direction by examining their goodness-of-fit under restricted model classes. In this paper, we describe a parametrization of bivariate SCMs in terms of a causal velocity by viewing the cause variable as time in a dynamical system. The velocity implicitly defines counterfactual curves via the solution of initial value problems where the observation specifies the initial condition. Using tools from measure transport, we obtain a unique correspondence between SCMs and the score function of the generated distribution via its causal velocity. Based on this, we derive an objective function that directly regresses the velocity against the score function, the latter of which can be estimated non-parametrically from observational data. We use this to develop a method for bivariate causal discovery that extends beyond known model classes such as additive or location scale noise, and that requires no assumptions on the noise distributions. When the score is estimated well, the objective is also useful for detecting model non-identifiability and misspecification. We present positive results in simulation and benchmark experiments where many existing methods fail, and perform ablation studies to examine the method's sensitivity to accurate score estimation.