{"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/two-sample-statistics-based-on-anisotropic","title":"Two-sample Statistics Based on Anisotropic Kernels","arxiv_id":"1709.05006","date":"2017-09-14","proceeding":null,"authors":["Xiuyuan Cheng","Alexander Cloninger","Ronald R. Coifman"],"abstract":"The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD)\nstatistic for measuring the distance between two distributions given\nfinitely-many multivariate samples. When the distributions are locally\nlow-dimensional, the proposed test can be made more powerful to distinguish\ncertain alternatives by incorporating local covariance matrices and\nconstructing an anisotropic kernel. The kernel matrix is asymmetric; it\ncomputes the affinity between $n$ data points and a set of $n_R$ reference\npoints, where $n_R$ can be drastically smaller than $n$. While the proposed\nstatistic can be viewed as a special class of Reproducing Kernel Hilbert Space\nMMD, the consistency of the test is proved, under mild assumptions of the\nkernel, as long as $\\|p-q\\| \\sqrt{n} \\to \\infty $, and a finite-sample lower\nbound of the testing power is obtained. Applications to flow cytometry and\ndiffusion MRI datasets are demonstrated, which motivate the proposed approach\nto compare distributions.","url_abs":"http://arxiv.org/abs/1709.05006v3","url_pdf":"http://arxiv.org/pdf/1709.05006v3.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":"two-sample-statistics-based-on-anisotropic","repo_url":"https://github.com/AClon42/two-sample-anisotropic","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"diffusion-mri","task_name":"Diffusion  MRI"},{"task_slug":"two","task_name":"Vocal Bursts Valence Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}