Differentially Private Two-Stage Empirical Risk Minimization with Applications to Individualized Treatment Rule
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917527523688448 |
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| author | Lee, Joowon Chen, Guanhua |
| author_facet | Lee, Joowon Chen, Guanhua |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12604 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Differentially Private Two-Stage Empirical Risk Minimization with Applications to Individualized Treatment Rule Lee, Joowon Chen, Guanhua Statistics Theory Machine Learning 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. |
| title | Differentially Private Two-Stage Empirical Risk Minimization with Applications to Individualized Treatment Rule |
| topic | Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2602.12604 |