Causal inference using invariant prediction: identification and confidence intervals

TL;DR

This paper introduces a method for causal inference based on the invariance of predictive accuracy across different experimental settings, providing confidence intervals for causal relationships, especially in complex scenarios like gene perturbation data.

Contribution

It proposes a novel invariance-based approach for causal inference that identifies causal predictors and constructs confidence intervals, applicable to general and complex models.

Findings

The method reliably identifies causal predictors across interventions.

It provides valid confidence intervals for causal effects.

Empirical tests demonstrate effectiveness on gene perturbation data.

Abstract

What is the difference of a prediction that is made with a causal model and a non-causal model? Suppose we intervene on the predictor variables or change the whole environment. The predictions from a causal model will in general work as well under interventions as for observational data. In contrast, predictions from a non-causal model can potentially be very wrong if we actively intervene on variables. Here, we propose to exploit this invariance of a prediction under a causal model for causal inference: given different experimental settings (for example various interventions) we collect all models that do show invariance in their predictive accuracy across settings and interventions. The causal model will be a member of this set of models with high probability. This approach yields valid confidence intervals for the causal relationships in quite general scenarios. We examine the example of structural equation models in more detail and provide sufficient assumptions under which the set of causal predictors becomes identifiable. We further investigate robustness properties of our approach under model misspecification and discuss possible extensions. The empirical properties are studied for various data sets, including large-scale gene perturbation experiments.