{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/differentially-private-covariance-revisited","title":"Differentially Private Covariance Revisited","arxiv_id":"2205.14324","date":"2022-05-28","proceeding":null,"authors":["Wei Dong","Yuting Liang","Ke Yi"],"abstract":"In this paper, we present two new algorithms for covariance estimation under concentrated differential privacy (zCDP). The first algorithm achieves a Frobenius error of $\\tilde{O}(d^{1/4}\\sqrt{\\mathrm{tr}}/\\sqrt{n} + \\sqrt{d}/n)$, where $\\mathrm{tr}$ is the trace of the covariance matrix. By taking $\\mathrm{tr}=1$, this also implies a worst-case error bound of $\\tilde{O}(d^{1/4}/\\sqrt{n})$, which improves the standard Gaussian mechanism's $\\tilde{O}(d/n)$ for the regime $d>\\widetilde{\\Omega}(n^{2/3})$. Our second algorithm offers a tail-sensitive bound that could be much better on skewed data. The corresponding algorithms are also simple and efficient. Experimental results show that they offer significant improvements over prior work.","url_abs":"https://arxiv.org/abs/2205.14324v3","url_pdf":"https://arxiv.org/pdf/2205.14324v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"differentially-private-covariance-revisited","repo_url":"https://github.com/hkustdb/privatecovariance","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"differentially-private-covariance-revisited","repo_url":"https://github.com/opencode2022/privatecovariance","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2205.14324","atlas_url":"https://app.syntology.ai/?focus=2205.14324","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}