Self-Compatibility: Evaluating Causal Discovery without Ground Truth
This addresses a critical issue for researchers in causal inference, offering a practical tool for validation in real-world scenarios where ground truth is unavailable, though it is incremental as it builds on existing causal discovery frameworks.
The paper tackles the problem of evaluating causal discovery algorithms without ground truth by proposing a method to falsify their outputs based on compatibility between graphs learned from different variable subsets, demonstrating its utility in causal model selection.
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.