Abstract:Differential privacy provides a formal framework for releasing statistical estimators that limit how much any single observation can influence the output, by injecting calibrated random noise. We study differentially private estimation in two-stage procedures common in causal inference and individualized treatment rule (ITR) learning, in which data-dependent weights are first estimated to enforce covariate balance and a parameter of interest is then obtained by weighted empirical risk minimization. We propose Differentially Private Two-Stage Empirical Risk Minimization (DP-2ERM), which privatizes the final estimator directly through objective perturbation calibrated to the data-dependent sensitivity of the full pipeline. The analysis combines deterministic weight-perturbation bounds for several covariate-balancing methods (inverse propensity weighting, entropy balancing weighting, and maximum mean discrepancy weighting) with probabilistic sensitivity bounds for the second-stage solution. The resulting calibration is sharper than the natural stage-wise composition baseline, which the same sensitivity analysis supplies as a byproduct. Simulation studies and a benchmark application to ITR learning demonstrate the improved privacy--utility trade-off.
| Comments: | 25 pages, 2 figures. Technical proofs are omitted for the initial version. It will be included in future versions |
| Subjects: | Statistics Theory (math.ST); Machine Learning (stat.ML) |
| Cite as: | arXiv:2602.12604 [math.ST] |
| (or arXiv:2602.12604v2 [math.ST] for this version) | |
| https://doi.org/10.48550/arXiv.2602.12604 arXiv-issued DOI via DataCite |
From: Joowon Lee [view email]
[v1]
Fri, 13 Feb 2026 04:22:46 UTC (1,714 KB)
[v2]
Sat, 23 May 2026 15:21:17 UTC (828 KB)
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