Risk-Calibrated Balancing for High-Dimensional Causal Extrapolation

2026-09-28

AI Summary

This study addresses the weight concentration and variance inflation problems in causal inference under high-dimensional weak overlap, which arise from covariate balancing. To tackle these issues, this work proposes an optimization framework based on ridge augmentation and conditional predictive risk calibration. Methodologically, it establishes a finite-sample risk decomposition theory and designs a target-aware consistent risk estimator to adaptively select optimal baseline weights. The approach further integrates ridge regression, random-effects prediction models, and proportional asymptotic analysis techniques. Both theoretical analyses and experimental evaluations demonstrate that the proposed method significantly reduces excess risk on simulated and empirical datasets. Moreover, it achieves superior performance in estimating average treatment effects under weak overlap scenarios compared to existing benchmark methods.

Abstract

In observational causal inference, covariate balancing is widely used to reduce source-target covariate shift, but under weak overlap in high dimensions, stronger balance can induce concentrated weights and increase variance. Balance measures how well the target covariate distribution is represented, but does not by itself determine how reliably the counterfactual mean can be estimated. We develop risk-calibrated balancing for the average treatment effect on the treated, which applies ridge augmentation to any normalised base weights and selects its penalty using conditional prediction risk of the counterfactual mean. Under a random-effects predictive model, we derive an exact finite-sample decomposition of this risk into residual covariate imbalance and weight-induced variance. For design-independent base weights under proportional asymptotics, we characterise how limiting risk depends on source and target covariance geometry, population mean shift, and weight concentration. For covariate-adaptive base weights, we develop a uniformly consistent target-aware risk estimator whose minimiser attains vanishing scaled oracle excess risk. Simulations show that the high-dimensional risk predictions remain informative for adaptive balancing and that target-aware tuning generally reduces excess target risk. Empirical analyses of job-training and single-cell perturbation data show that risk-calibrated balancing generally improves on the corresponding base estimators, with larger gains under weaker overlap.

Problem

• causal extrapolation
• covariate balancing
• high-dimensional
• weak overlap
• counterfactual mean estimation

Innovation

• risk-calibrated balancing
• high-dimensional causal extrapolation
• ridge augmentation
• covariate imbalance
• oracle excess risk