Variance-Efficient Adjustment for High-Dimensional Causal Inference

Variable selection for causal inference typically prioritizes unbiasedness by identifying a valid adjustment set. In high-dimensional settings, where there are more covariates than samples, valid adjustment sets can be suboptimal in terms of treatment effect MSE, as they ignore the bias-variance trade-off. To address this, we propose VERA (Variance-Efficient Relaxed Adjustment), a variable selection component designed to wrap around any differentiable causal estimator. VERA selects variables via a differentiable gating mechanism, learning inclusion probabilities for each covariate. The selection is optimized to reduce the variance of the Efficient Influence Function, which prioritizes variables that explain more variation in the outcome than variation in the treatment. In our experiments, VERA improves the finite-sample estimation error of various base estimators in most settings, particularly in high-dimensional and small-sample regimes.