Causal inference using invariant prediction: identification and confidence intervals
This work addresses the challenge of reliable causal inference for researchers in fields like biology and statistics, offering a novel approach but with incremental elements building on invariance concepts.
The paper tackles the problem of distinguishing causal from non-causal models by exploiting invariance in predictive accuracy across interventions, proposing a method that yields valid confidence intervals for causal relationships. It demonstrates empirical properties on datasets like gene perturbation experiments, showing applicability in general scenarios.
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.