{"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/kernel-based-tests-for-likelihood-free","title":"Kernel-Based Tests for Likelihood-Free Hypothesis Testing","arxiv_id":"2308.09043","date":"2023-08-17","proceeding":"NeurIPS 2023 11","authors":["Patrik Róbert Gerber","Tianze Jiang","Yury Polyanskiy","Rui Sun"],"abstract":"Given $n$ observations from two balanced classes, consider the task of labeling an additional $m$ inputs that are known to all belong to \\emph{one} of the two classes. Special cases of this problem are well-known: with complete knowledge of class distributions ($n=\\infty$) the problem is solved optimally by the likelihood-ratio test; when $m=1$ it corresponds to binary classification; and when $m\\approx n$ it is equivalent to two-sample testing. The intermediate settings occur in the field of likelihood-free inference, where labeled samples are obtained by running forward simulations and the unlabeled sample is collected experimentally. In recent work it was discovered that there is a fundamental trade-off between $m$ and $n$: increasing the data sample $m$ reduces the amount $n$ of training/simulation data needed. In this work we (a) introduce a generalization where unlabeled samples come from a mixture of the two classes -- a case often encountered in practice; (b) study the minimax sample complexity for non-parametric classes of densities under \\textit{maximum mean discrepancy} (MMD) separation; and (c) investigate the empirical performance of kernels parameterized by neural networks on two tasks: detection of the Higgs boson and detection of planted DDPM generated images amidst CIFAR-10 images. For both problems we confirm the existence of the theoretically predicted asymmetric $m$ vs $n$ trade-off.","url_abs":"https://arxiv.org/abs/2308.09043v2","url_pdf":"https://arxiv.org/pdf/2308.09043v2.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":"kernel-based-tests-for-likelihood-free","repo_url":"https://github.com/sr-11/lfi","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"binary-classification","task_name":"Binary Classification"},{"task_slug":"hypothesis-testing","task_name":"Two-sample testing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}