{"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/differential-privacy-of-dirichlet-posterior","title":"Dirichlet Mechanism for Differentially Private KL Divergence Minimization","arxiv_id":"2110.01984","date":"2021-10-03","proceeding":"NeurIPS 2021 12","authors":["Donlapark Ponnoprat"],"abstract":"Given an empirical distribution $f(x)$ of sensitive data $x$, we consider the task of minimizing $F(y) = D_{\\text{KL}} (f(x)\\Vert y)$ over a probability simplex, while protecting the privacy of $x$. We observe that, if we take the exponential mechanism and use the KL divergence as the loss function, then the resulting algorithm is the Dirichlet mechanism that outputs a single draw from a Dirichlet distribution. Motivated by this, we propose a R\\'enyi differentially private (RDP) algorithm that employs the Dirichlet mechanism to solve the KL divergence minimization task. In addition, given $f(x)$ as above and $\\hat{y}$ an output of the Dirichlet mechanism, we prove a probability tail bound on $D_{\\text{KL}} (f(x)\\Vert \\hat{y})$, which is then used to derive a lower bound for the sample complexity of our RDP algorithm. Experiments on real-world datasets demonstrate advantages of our algorithm over Gaussian and Laplace mechanisms in supervised classification and maximum likelihood estimation.","url_abs":"https://arxiv.org/abs/2110.01984v3","url_pdf":"https://arxiv.org/pdf/2110.01984v3.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":"differential-privacy-of-dirichlet-posterior","repo_url":"https://github.com/dirsampling/privatedps","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"differential-privacy-of-dirichlet-posterior","repo_url":"https://github.com/donlapark/dirichlet-mechanism","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"privacy-preserving","task_name":"Privacy Preserving"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}