🤖 AI Summary
This study addresses the challenge of efficiently estimating causal effects under confounding when experimental budgets are limited. The authors propose a novel approach that integrates instrumental variable regression with Gaussian graphical models, leveraging prior knowledge of partial joint distributions to optimize the allocation between fully observed samples and partially observed data (e.g., only \(X_{12}\)). Under a fixed budget constraint, this method analytically derives the optimal sampling scheme that minimizes the asymptotic variance of the causal effect estimator—a solution not previously available in closed form. Theoretical analysis demonstrates that the proposed allocation significantly reduces both the total budget and the number of complete observations required to detect non-zero causal effects. Empirical validation in automotive analytics and drug discovery underscores the method’s practical utility alongside its theoretical contributions.
📝 Abstract
Instrumental variable regression quantifies causal effects between a possibly confounded treatment variable $ X_2 $ and a response variable $ X_3 $ by leveraging an instrument $ X_1 $. Our work considers the setting where some prior information of the joint distribution of $ X_{123} $ is given, potentially through an initial dataset. However, further samples must be gathered to improve the accuracy of the estimation. We show that under specific parameter configurations in a Gaussian graphical model, taking partial samples from, e.g., $ X_{12} $ can reduce the asymptotic variance of a consistent estimator. This idea is developed by adding a budget constraint over the cost per (partial) sample. The optimization problem is analytically solvable over the real numbers and gives the optimal number of requested partial and complete samples. We provide significance level, power, and sample-size calculations for detecting a non-zero causal effect under optimal budget allocation. Our method can considerably reduce the necessary budget and the number of complete samples. Finally, we showcase the advantages and applicability of adaptive causal effect estimation for automotive analytics and pharmaceutical research.