MSE-optimal adjustment sets in linear Gaussian causal models with finite sample size

Nadja Rutsch, Sara Magliacane, Stéphanie L. van der Pas

Keywords: Adjustment set, Average treatment effect, Causality, Efficiency, Graphical model, Ordinary least-squares estimator

Abstract: Covariate selection for causal inference based on the causal graph commonly aims for unbiasedness and asymptotic efficiency of the causal effect estimator. When the sample size is finite, these approaches can lead to results that are suboptimal in terms of the Mean Squared Error (MSE). We aim to find the adjustment set that is optimal in terms of MSE, taking into account the joint distribution of the causal variables and the sample size. We present examples where the MSE-optimal adjustment set differs from the optimal adjustment set, depending on the sample size. To find the MSE-optimal adjustment set, we introduce a sample size criterion that compares two adjustment sets in linear Gaussian models. We develop graphical criteria to reduce the search space for this adjustment set based on the causal graph. In preliminary experiments, we show that the estimated MSE-optimal adjustment set can outperform the optimal adjustment set in finite sample size settings, and performs competitively in larger sample size settings.

Submission Number: 8