Sample Observed Effects: Enumeration, Randomization and Generalization
This work addresses the challenge of external validity in causal inference, which is crucial for researchers and practitioners in fields like epidemiology and social sciences, though it appears incremental by building on existing counterfactual frameworks.
The paper tackles the problem of generalizing causal effects beyond the original sample by proposing a combinatorial definition for external validity, revealing that generalization is possible when effects are observed under all enumerable backgrounds or when backgrounds are sufficiently randomized. It demonstrates tradeoffs in performance for various estimators and applies the framework to incomplete samples like those from the COVID-19 pandemic.
The widely used 'Counterfactual' definition of Causal Effects was derived for unbiasedness and accuracy - and not generalizability. We propose a Combinatorial definition for the External Validity (EV) of intervention effects. We first define the concept of an effect observation 'background'. We then formulate conditions for effect generalization based on samples' sets of (observed and unobserved) backgrounds. This reveals two limits for effect generalization: (1) when effects of a variable are observed under all their enumerable backgrounds, or, (2) when backgrounds have become sufficiently randomized. We use the resulting combinatorial framework to re-examine several issues in the original counterfactual formulation: out-of-sample validity, concurrent estimation of multiple effects, bias-variance tradeoffs, statistical power, and connections to current predictive and explaining techniques. Methodologically, the definitions also allow us to replace the parametric estimation problems that followed the counterfactual definition by combinatorial enumeration and randomization problems in non-experimental samples. We use the resulting non-parametric framework to demonstrate (External Validity, Unconfoundness and Precision) tradeoffs in the performance of popular supervised, explaining, and causal-effect estimators. We also illustrate how the approach allows for the use of supervised and explaining methods in non-i.i.d. samples. The COVID19 pandemic highlighted the need for learning solutions to provide predictions in severally incomplete samples. We demonstrate applications in this pressing problem.