New paper proposes optimal control variates for variance reduction in survey sampling and causal inference

RexDouglass · x · 2026-08-18

The paper proposes a family of control variate estimators for variance reduction in design-based survey sampling and causal inference, with and without interference. In these settings, inverse probability weighting (IPW) estimators are widely used but may have large variance when sampling, treatment, or exposure probabilities are small. Building on the observation that several common estimators (Hajek, normalized, and augmented IPW) correct the Horvitz-Thompson estimator by canceling part of its randomness, the paper provides a unified interpretation of these estimators as special cases of a general control variate estimator. It then constructs optimal control variates that can further reduce finite sample variance. The optimal bases are characterized through a stochastic optimization formulation. In survey sampling and causal inference without interference, the optimal bases are characterized by leading eigenvectors of matrices depending on both design-based sampling structure and model-based outcome uncertainty. In causal inference under network interference, the optimal bases solve a nonconvex quadratic optimization problem; a 1/2-approximate solution and an alternating local search heuristic are provided. The estimators are applied to the Swiss Environmental Panel survey data and Chinese social network data, with extensive experiments.

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New paper proposes optimal control variates for variance reduction in survey sampling and causal inference

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