Distinguishing Cause from Effect with Causal Velocity Models

2025-02-07

AI Summary

This paper addresses causal direction identification in binary structural causal models (SCMs), proposing a novel assumption-free method based on the concept of “causal speed.” The approach models causal inference as a dynamical system: causal speed is defined with respect to the cause variable as the time axis, and a unique mapping between SCMs and distribution score functions is established via measure transport—bypassing conventional assumptions such as additive or location-scale noise. This work introduces causal speed for the first time, enabling nonparametric score estimation and well-posed initial-value problem solving, while automatically detecting model unidentifiability and misspecification. In extensive simulations and benchmark evaluations, the method significantly outperforms state-of-the-art approaches, particularly under challenging conditions—e.g., nonstandard noise distributions and nonlinear SCMs—where existing methods fail. Ablation studies confirm strong robustness to score estimation quality.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Distinguish cause from effect
• Parametrize bivariate SCMs
• Develop bivariate causal discovery method

Innovation

• Parametrization using causal velocity
• Measure transport for unique correspondence
• Non-parametric score function regression