MODE: Minimax Optimal Deterministic Experiments for Causal Inference in the Presence of Covariates

Area of Science:

• Statistics
• Causal Inference
• Experimental Design

Background:

• Data-driven decision-making relies on accurate causal effect estimation.
• Randomization and re-randomization are common but can be suboptimal with many covariates.
• Existing methods may not effectively minimize covariate discrepancies between groups.

Purpose of the Study:

• To quantify the worst-case mean squared error of the difference-in-means estimator.
• To introduce a novel optimal deterministic experiment for minimizing covariate discrepancy.
• To demonstrate the superiority of the proposed method over existing randomized approaches.

Main Methods:

• Quantified generalized discrepancy using worst-case mean squared error.
• Developed an optimal deterministic experiment leveraging quasi-Monte Carlo techniques.
• Provided theoretical proof of faster convergence using Mahalanobis distance.

Main Results:

• Existing randomized experiments using Monte Carlo methods are sub-optimal.
• The proposed quasi-Monte Carlo experiment minimizes generalized discrepancy effectively.
• The difference-in-means estimator from the proposed experiment shows faster convergence.
• Simulations confirm reduced covariate imbalance and estimation uncertainty.

Conclusions:

• The novel deterministic experiment offers a reliable framework for causal inference.
• Quasi-Monte Carlo techniques enhance covariate balance and reduce estimation error.
• This approach optimizes controlled experimentation for data-driven decisions.