Sample Observed Effects: Enumeration, Randomization and Generalization

TL;DR

This paper introduces a combinatorial framework for assessing the external validity of causal effects, emphasizing enumeration and randomization to improve generalization and applicability in non-experimental and incomplete samples.

Contribution

It proposes a novel combinatorial definition of external validity and re-examines counterfactual issues, enabling non-parametric enumeration and randomization approaches for causal inference.

Findings

Reveals limits for effect generalization based on backgrounds

Demonstrates tradeoffs in estimator performance in non-i.i.d. samples

Shows applications in incomplete data scenarios like COVID-19

Abstract

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.