{"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/near-optimal-model-discrimination-with-non","title":"Near-Optimal Procedures for Model Discrimination with Non-Disclosure Properties","arxiv_id":"2012.02901","date":"2020-12-04","proceeding":null,"authors":["Dmitrii M. Ostrovskii","Mohamed Ndaoud","Adel Javanmard","Meisam Razaviyayn"],"abstract":"Let $\\theta_0,\\theta_1 \\in \\mathbb{R}^d$ be the population risk minimizers associated to some loss $\\ell:\\mathbb{R}^d\\times \\mathcal{Z}\\to\\mathbb{R}$ and two distributions $\\mathbb{P}_0,\\mathbb{P}_1$ on $\\mathcal{Z}$. The models $\\theta_0,\\theta_1$ are unknown, and $\\mathbb{P}_0,\\mathbb{P}_1$ can be accessed by drawing i.i.d samples from them. Our work is motivated by the following model discrimination question: \"What sizes of the samples from $\\mathbb{P}_0$ and $\\mathbb{P}_1$ allow to distinguish between the two hypotheses $\\theta^*=\\theta_0$ and $\\theta^*=\\theta_1$ for given $\\theta^*\\in\\{\\theta_0,\\theta_1\\}$?\" Making the first steps towards answering it in full generality, we first consider the case of a well-specified linear model with squared loss. Here we provide matching upper and lower bounds on the sample complexity as given by $\\min\\{1/\\Delta^2,\\sqrt{r}/\\Delta\\}$ up to a constant factor; here $\\Delta$ is a measure of separation between $\\mathbb{P}_0$ and $\\mathbb{P}_1$ and $r$ is the rank of the design covariance matrix. We then extend this result in two directions: (i) for general parametric models in asymptotic regime; (ii) for generalized linear models in small samples ($n\\le r$) under weak moment assumptions. In both cases we derive sample complexity bounds of a similar form while allowing for model misspecification. In fact, our testing procedures only access $\\theta^*$ via a certain functional of empirical risk. In addition, the number of observations that allows us to reach statistical confidence does not allow to \"resolve\" the two models $-$ that is, recover $\\theta_0,\\theta_1$ up to $O(\\Delta)$ prediction accuracy. These two properties allow to use our framework in applied tasks where one would like to $\\textit{identify}$ a prediction model, which can be proprietary, while guaranteeing that the model cannot be actually $\\textit{inferred}$ by the identifying agent.","url_abs":"https://arxiv.org/abs/2012.02901v3","url_pdf":"https://arxiv.org/pdf/2012.02901v3.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":"near-optimal-model-discrimination-with-non","repo_url":"https://github.com/ostrodmit/testing-without-recovery","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}