{"ID":3050129,"CreatedAt":"2026-06-04T02:13:16.786527022Z","UpdatedAt":"2026-06-06T08:58:50.400332682Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.04683","arxiv_id":"2606.04683","title":"Minimax Private Estimation of Smooth Optimal-Transport Maps","abstract":"We study the problem of estimating smooth optimal transport (OT) maps between two probability distributions under differential privacy (DP) constraints. Leveraging wavelet-based density estimators and recent stability bounds for smooth OT maps, we propose differentially private estimators that apply to both central and local DP models. Our main estimator achieves near-minimax optimal rates in dimension $d \\geq 2$, and we complement it with a quantile-based estimator that attains minimax optimal rates in dimension $d = 1$ under central DP. We further establish matching minimax lower bounds, confirming the near-optimality of our approach. To the best of our knowledge, this constitutes the first differentially private procedure for OT map estimation with minimax optimality guarantees.","short_abstract":"We study the problem of estimating smooth optimal transport (OT) maps between two probability distributions under differential privacy (DP) constraints. Leveraging wavelet-based density estimators and recent stability bounds for smooth OT maps, we propose differentially private estimators that apply to both central and...","url_abs":"https://arxiv.org/abs/2606.04683","url_pdf":"https://arxiv.org/pdf/2606.04683v1","authors":"[\"Clément Lalanne\",\"David Rodríguez-Vítores\",\"Franck Iutzeler\",\"Jean-Michel Loubes\"]","published":"2026-06-03T10:05:10Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}