{"paper":{"title":"On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR","cs.DS","math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Kevin Tian, Purnamrita Sarkar, Shourya Pandey, Syamantak Kumar","submitted_at":"2026-06-20T08:38:51Z","abstract_excerpt":"We study high-dimensional differentially private (DP) covariance estimation in the operator norm, and principal component analysis (PCA), under $k$-row-column sparsity ($k$-RCS) of the covariance matrix. In the non-private setting, it is known that $\\mathsf{poly}(k, \\log d)$ samples suffice to solve both of these problems. However, the only comparable result known under DP (Wang et al. 2021) requires $\\Omega(d)$ samples under standard parameterizations of the problem. We investigate when this curse of dimensionality is inherent for sparse covariance estimation tasks under DP.\n  On the upper bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21951","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.21951/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}