dorsal/arxiv
View SchemaDifferentially Private Inference for Longitudinal Linear Regression
| Authors | Getoar Sopa, Marco Avella Medina, Cynthia Rush |
|---|---|
| Categories | |
| ArXiv ID | 2601.10626vv1 |
| URL | https://arxiv.org/abs/2601.10626 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
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.
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"date_created": "2026-02-17T05:53:26.456000Z",
"date_modified": "2026-02-17T05:53:26.456000Z",
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"record": {
"abstract": "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\u0027s 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.",
"arxiv_id": "2601.10626",
"authors": [
"Getoar Sopa",
"Marco Avella Medina",
"Cynthia Rush"
],
"categories": [
"math.ST",
"cs.CR",
"stat.ME",
"stat.ML",
"stat.TH"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Differentially Private Inference for Longitudinal Linear Regression",
"url": "https://arxiv.org/abs/2601.10626",
"version": "v1"
},
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