ABC3: Active Bayesian Causal Inference with Cohn Criteria in Randomized Experiments

TL;DR

ABC3 introduces a Bayesian active learning approach for causal inference in randomized experiments, optimizing experimental design by minimizing estimation error and imbalance, leading to higher efficiency.

Contribution

The paper presents ABC3, a novel Bayesian active learning policy that minimizes estimation error and imbalance, with theoretical guarantees and superior empirical performance.

Findings

ABC3 achieves the highest efficiency in real-world experiments.

The policy minimizes integrated posterior variance and imbalance.

Theoretical proofs confirm error and imbalance minimization.

Abstract

In causal inference, randomized experiment is a de facto method to overcome various theoretical issues in observational study. However, the experimental design requires expensive costs, so an efficient experimental design is necessary. We propose ABC3, a Bayesian active learning policy for causal inference. We show a policy minimizing an estimation error on conditional average treatment effect is equivalent to minimizing an integrated posterior variance, similar to Cohn criteria \citep{cohn1994active}. We theoretically prove ABC3 also minimizes an imbalance between the treatment and control groups and the type 1 error probability. Imbalance-minimizing characteristic is especially notable as several works have emphasized the importance of achieving balance. Through extensive experiments on real-world data sets, ABC3 achieves the highest efficiency, while empirically showing the theoretical results hold.