🤖 AI Summary
This study addresses the high computational cost of double machine learning (DML) with large-scale observational data and the inadequacy of simple random subsampling, which often results in insufficient covariate coverage and imbalance between treatment and control groups. The authors propose UD-DML, a novel subsampling approach that incorporates uniform design principles into DML for the first time. The method first applies PCA rotation to covariates, then constructs a low-discrepancy skeleton based on a hybrid discrepancy criterion, and finally uses KD-trees to match nearest-neighbor treated and control units to each skeleton point, yielding a representative and balanced subsample. Theoretical analysis establishes that UD-DML retains √n-asymptotic normality even when the subsample size is much smaller than the full dataset. Experiments demonstrate that, compared to uniform sampling, UD-DML achieves lower RMSE, narrower confidence intervals, and more reliable coverage—particularly under low overlap and model misspecification.
📝 Abstract
Double machine learning (DML) delivers valid inference on low-dimensional causal parameters while permitting flexible nuisance estimation, but its computational cost becomes prohibitive once cross-fitted learners must be trained on massive observational data. Applying DML to a uniformly drawn subsample alleviates this burden, yet such a reduction disregards the geometry of the covariate space and can exacerbate treated-control imbalance as well as overlap deficiency. We propose Uniform Design Double Machine Learning (UD-DML), a design-based subsampling strategy for average treatment effect (ATE) estimation. UD-DML first constructs a low-discrepancy skeleton in a PCA-rotated covariate space under the mixture-discrepancy criterion, and then assigns, to each skeleton point, the nearest treated and control units via KD-tree search. The resulting matched subsample is, by construction, both representative of the full covariate distribution and balanced across treatment arms; cross-fitted DML is subsequently applied to it. We establish discrepancy-based guarantees for representativeness and balance, and prove that the UD-DML estimator is $\sqrt{r}$-asymptotically normal under mild conditions, where the selected subsample size $r \ll n$. The dominant nuisance-fitting cost is thereby reduced from the $n$-scale to the $r$-scale. Monte Carlo experiments show that UD-DML attains lower RMSE, narrower confidence intervals and more reliable coverage than uniform subsampling, with the largest gains in low-overlap and misspecified regimes. An application to a large observational dataset further demonstrates its practical feasibility.