Differentially Private Inference for Longitudinal Linear Regression
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911377729257472 |
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| author | Sopa, Getoar Medina, Marco Avella Rush, Cynthia |
| author_facet | Sopa, Getoar Medina, Marco Avella Rush, Cynthia |
| contents | Differential Privacy (DP) provides a rigorous framework for releasing statistics while protecting individual information present in a dataset. Although substantial progress has been made on differentially private linear regression, existing methods almost exclusively address the item-level DP setting, where each user contributes a single observation. Many scientific and economic applications instead involve longitudinal or panel data, in which each user contributes multiple dependent observations. In these settings, item-level DP offers inadequate protection, and user-level DP - shielding an individual's entire trajectory - is the appropriate privacy notion. We develop a comprehensive framework for estimation and inference in longitudinal linear regression under user-level DP. We propose a user-level private regression estimator based on aggregating local regressions, and we establish finite-sample guarantees and asymptotic normality under short-range dependence. For inference, we develop a privatized, bias-corrected covariance estimator that is automatically heteroskedasticity- and autocorrelation-consistent. These results provide the first unified framework for practical user-level DP estimation and inference in longitudinal linear regression under dependence, with strong theoretical guarantees and promising empirical performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10626 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Differentially Private Inference for Longitudinal Linear Regression Sopa, Getoar Medina, Marco Avella Rush, Cynthia Statistics Theory Cryptography and Security Methodology Machine Learning Differential Privacy (DP) provides a rigorous framework for releasing statistics while protecting individual information present in a dataset. Although substantial progress has been made on differentially private linear regression, existing methods almost exclusively address the item-level DP setting, where each user contributes a single observation. Many scientific and economic applications instead involve longitudinal or panel data, in which each user contributes multiple dependent observations. In these settings, item-level DP offers inadequate protection, and user-level DP - shielding an individual's entire trajectory - is the appropriate privacy notion. We develop a comprehensive framework for estimation and inference in longitudinal linear regression under user-level DP. We propose a user-level private regression estimator based on aggregating local regressions, and we establish finite-sample guarantees and asymptotic normality under short-range dependence. For inference, we develop a privatized, bias-corrected covariance estimator that is automatically heteroskedasticity- and autocorrelation-consistent. These results provide the first unified framework for practical user-level DP estimation and inference in longitudinal linear regression under dependence, with strong theoretical guarantees and promising empirical performance. |
| title | Differentially Private Inference for Longitudinal Linear Regression |
| topic | Statistics Theory Cryptography and Security Methodology Machine Learning |
| url | https://arxiv.org/abs/2601.10626 |