{"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/learning-deep-kernels-for-non-parametric-two","title":"Learning Deep Kernels for Non-Parametric Two-Sample Tests","arxiv_id":"2002.09116","date":"2020-02-21","proceeding":"ICML 2020 1","authors":["Feng Liu","Wenkai Xu","Jie Lu","Guangquan Zhang","Arthur Gretton","Danica J. Sutherland"],"abstract":"We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test power. These tests adapt to variations in distribution smoothness and shape over space, and are especially suited to high dimensions and complex data. By contrast, the simpler kernels used in prior kernel testing work are spatially homogeneous, and adaptive only in lengthscale. We explain how this scheme includes popular classifier-based two-sample tests as a special case, but improves on them in general. We provide the first proof of consistency for the proposed adaptation method, which applies both to kernels on deep features and to simpler radial basis kernels or multiple kernel learning. In experiments, we establish the superior performance of our deep kernels in hypothesis testing on benchmark and real-world data. The code of our deep-kernel-based two sample tests is available at https://github.com/fengliu90/DK-for-TST.","url_abs":"https://arxiv.org/abs/2002.09116v3","url_pdf":"https://arxiv.org/pdf/2002.09116v3.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":"learning-deep-kernels-for-non-parametric-two","repo_url":"https://github.com/fengliu90/DK-for-TST","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"hypothesis-testing","task_name":"Two-sample testing"},{"task_slug":"two","task_name":"Vocal Bursts Valence Prediction"}],"methods":[{"method_slug":"test","method_name":"Test"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/two-sample-testing-on-blob-9-modes-40-for","task":"Two-sample testing","dataset":"Blob (9 modes, 40 for each)","model":"MMD-D","rank_in_archive_order":1,"of":1,"metrics":{"Avg accuracy":"98.5"},"uses_additional_data":false},{"leaderboard":"/sota/two-sample-testing-on-cifar-10-vs-cifar-10-1-1","task":"Two-sample testing","dataset":"CIFAR-10 vs CIFAR-10.1 (1000 samples)","model":"MMD-D","rank_in_archive_order":1,"of":1,"metrics":{"Avg accuracy":"74.4"},"uses_additional_data":false},{"leaderboard":"/sota/two-sample-testing-on-hdgm-d-10-n-4000","task":"Two-sample testing","dataset":"HDGM (d=10, N=4000)","model":"MMD-D","rank_in_archive_order":1,"of":1,"metrics":{"Avg accuracy":"65.9"},"uses_additional_data":false},{"leaderboard":"/sota/two-sample-testing-on-higgs-data-set","task":"Two-sample testing","dataset":"HIGGS Data Set","model":"MMD-D","rank_in_archive_order":1,"of":1,"metrics":{"Avg accuracy":"57.9"},"uses_additional_data":false},{"leaderboard":"/sota/two-sample-testing-on-mnist-vs-fake-mnist","task":"Two-sample testing","dataset":"MNIST vs Fake MNIST","model":"MMD-D","rank_in_archive_order":1,"of":1,"metrics":{"Avg accuracy":"91"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2002.09116","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2002.09116"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/fengliu90/DK-for-TST","reach":null}],"summary":{"ran_honours":1,"ran_fixture":1},"by_repo_kind":{"official":{"samples":2,"ran":2,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"a3acb8394ba06232","entry":"sample_blobs","repo":"fengliu90/DK-for-TST","repo_kind":"official","path":"Deep_Kernel_Blob.py","file_url":"https://github.com/fengliu90/DK-for-TST/blob/HEAD/Deep_Kernel_Blob.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"a3acb8394ba06232"}},{"code_sha256_prefix":"6a1eef89fc731e0f","entry":"sample_blobs_Q","repo":"fengliu90/DK-for-TST","repo_kind":"official","path":"Deep_Kernel_Blob.py","file_url":"https://github.com/fengliu90/DK-for-TST/blob/HEAD/Deep_Kernel_Blob.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"6a1eef89fc731e0f"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}