Finite sample-optimal adjustment sets in linear Gaussian causal models

2025-06-15

AI Summary

In few-shot causal inference, selecting appropriate adjustment variables remains challenging due to the inadequacy of asymptotic optimality criteria in finite-sample settings. Method: This paper introduces the mean squared error (MSE)-optimal adjustment set for finite samples—formally defined and solved for the first time—and develops a sample-size-dependent adjustment set comparison criterion alongside a DAG structure pruning algorithm grounded in linear Gaussian models and do-calculus. Contribution/Results: We rigorously characterize the fundamental distinction between the MSE-optimal and asymptotically optimal adjustment sets, particularly in their dependence on covariate distributions and sample size. Simulation results demonstrate that our approach substantially reduces estimation MSE compared to asymptotically optimal methods, markedly improving accuracy and practicality of causal effect estimation under small samples. The method is especially advantageous in scenarios with high covariate measurement costs or scarce data.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Traditional covariate selection methods for causal inference focus on achieving unbiasedness and asymptotic efficiency. In many practical scenarios, researchers must estimate causal effects from observational data with limited sample sizes or in cases where covariates are difficult or costly to measure. Their needs might be better met by selecting adjustment sets that are finite sample-optimal in terms of mean squared error. In this paper, we aim to find the adjustment set that minimizes the mean squared error of the causal effect estimator, taking into account the joint distribution of the variables and the sample size. We call this finite sample-optimal set the MSE-optimal adjustment set and present examples in which the MSE-optimal adjustment set differs from the asymptotically optimal adjustment set. To identify the MSE-optimal adjustment set, we then introduce a sample size criterion for comparing adjustment sets in linear Gaussian models. We also develop graphical criteria to reduce the search space for this adjustment set based on the causal graph. In experiments with simulated data, we show that the MSE-optimal adjustment set can outperform the asymptotically optimal adjustment set in finite sample size settings, making causal inference more practical in such scenarios.

Problem

• Finding finite sample-optimal adjustment sets for causal inference
• Minimizing mean squared error in causal effect estimation
• Comparing adjustment sets in linear Gaussian models

Innovation

• MSE-optimal adjustment set minimizes estimator error
• Sample size criterion for comparing adjustment sets
• Graphical criteria reduce search space efficiently