Self-Compatibility: Evaluating Causal Discovery without Ground Truth

TL;DR

This paper introduces a new method for evaluating causal discovery algorithms without ground truth by testing the stability of causal graphs across variable subsets, helping to identify incorrect causal inferences.

Contribution

It proposes a novel compatibility-based approach to falsify causal models, addressing the challenge of evaluating causal discovery without relying on simulated data.

Findings

Detecting incompatibilities can falsify incorrect causal relations.

Compatibility tests can aid in causal model selection.

The method provides strong evidence for causal models when compatibility implies distributional implications.

Abstract

As causal ground truth is incredibly rare, causal discovery algorithms are commonly only evaluated on simulated data. This is concerning, given that simulations reflect preconceptions about generating processes regarding noise distributions, model classes, and more. In this work, we propose a novel method for falsifying the output of a causal discovery algorithm in the absence of ground truth. Our key insight is that while statistical learning seeks stability across subsets of data points, causal learning should seek stability across subsets of variables. Motivated by this insight, our method relies on a notion of compatibility between causal graphs learned on different subsets of variables. We prove that detecting incompatibilities can falsify wrongly inferred causal relations due to violation of assumptions or errors from finite sample effects. Although passing such compatibility tests is only a necessary criterion for good performance, we argue that it provides strong evidence for the causal models whenever compatibility entails strong implications for the joint distribution. We also demonstrate experimentally that detection of incompatibilities can aid in causal model selection.