When Prediction Error Is Not Enough: Evaluating Nuisance-Function Prediction for Causal Estimation
arXiv:2609.00071v1 Announce Type: new Abstract: Prediction error is widely used to evaluate nuisance-function estimators in causal inference, but its relationship with causal estimator performance may differ across performance measures. We studied this question in a partially linear model using Monte Carlo simulations. We compared ordinary least squares (OLS), generalized additive models (GAMs), XGBoost, and Double Machine Learning with XGBoost (DML-XGBoost), evaluating nuisance-function prediction error, bias, RMSE, and 95\% confidence interval coverage. We also examined a simple joint-error measure based on the absolute cross-product of estimation errors from the exposure and outcome nuisance functions. Across the simulated settings, XGBoost had the lowest RMSE among the non-oracle methods, while DML-XGBoost generally provided better confidence interval coverage. Prediction error did not consistently track causal bias across methods and settings, and the method with the best point-estimation performance did not necessarily have the best confidence interval coverage. The joint-error measure was only weakly associated with causal bias and did not provide a useful standalone measure of causal performance. These results suggest that prediction error is useful for assessing nuisance-function estimation, but it should not be treated as a direct measure of the quality of the resulting causal estimator.
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[Submitted on 30 Aug 2026]
Title:When Prediction Error Is Not Enough: Evaluating Nuisance-Function Prediction for Causal Estimation
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Abstract:Prediction error is widely used to evaluate nuisance-function estimators in causal inference, but its relationship with causal estimator performance may differ across performance measures. We studied this question in a partially linear model using Monte Carlo simulations. We compared ordinary least squares (OLS), generalized additive models (GAMs), XGBoost, and Double Machine Learning with XGBoost (DML-XGBoost), evaluating nuisance-function prediction error, bias, RMSE, and 95\% confidence interval coverage. We also examined a simple joint-error measure based on the absolute cross-product of estimation errors from the exposure and outcome nuisance functions. Across the simulated settings, XGBoost had the lowest RMSE among the non-oracle methods, while DML-XGBoost generally provided better confidence interval coverage. Prediction error did not consistently track causal bias across methods and settings, and the method with the best point-estimation performance did not necessarily have the best confidence interval coverage. The joint-error measure was only weakly associated with causal bias and did not provide a useful standalone measure of causal performance. These results suggest that prediction error is useful for assessing nuisance-function estimation, but it should not be treated as a direct measure of the quality of the resulting causal estimator.
Comments: 10 pages, 2 figures, 1 table
Subjects:
Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Methodology (stat.ME)
Cite as: arXiv:2609.00071 [cs.AI]
(or arXiv:2609.00071v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.00071
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Cong Cao [view email] [v1] Sun, 30 Aug 2026 20:01:15 UTC (1,912 KB)
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