{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:PWPJXMT5A6DI5S7NP32OKTJPYW","short_pith_number":"pith:PWPJXMT5","schema_version":"1.0","canonical_sha256":"7d9e9bb27d07868ecbed7ef4e54d2fc5a8ab0ecf438908df06ba775ea49ad637","source":{"kind":"arxiv","id":"2506.01718","version":1},"attestation_state":"computed","paper":{"title":"Signature Maximum Mean Discrepancy Two-Sample Statistical Tests","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.DS"],"primary_cat":"stat.ML","authors_text":"Andrew Alden, Blanka Horvath, Zacharia Issa","submitted_at":"2025-06-02T14:26:58Z","abstract_excerpt":"Maximum Mean Discrepancy (MMD) is a widely used concept in machine learning research which has gained popularity in recent years as a highly effective tool for comparing (finite-dimensional) distributions. Since it is designed as a kernel-based method, the MMD can be extended to path space valued distributions using the signature kernel. The resulting signature MMD (sig-MMD) can be used to define a metric between distributions on path space. Similarly to the original use case of the MMD as a test statistic within a two-sample testing framework, the sig-MMD can be applied to determine if two se"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.01718","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-02T14:26:58Z","cross_cats_sorted":["cs.LG","math.DS"],"title_canon_sha256":"4ee2750be3dbfd0323ac4d14525e8f8d332759f2e74e3505228a0ad40e904ad1","abstract_canon_sha256":"5b5779a10a6ed7c811343700cc7f38384269f803a277426098e2c71b30cc6172"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:14:18.325761Z","signature_b64":"Bk9JSDuN/zk+hVE6V89FYnp+zyn1lzFibwjcF1Jo/Rcu8fpOvYgE6Yjfj3DQ65eRqpIYZEd6UQ6OKtQx6KA2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d9e9bb27d07868ecbed7ef4e54d2fc5a8ab0ecf438908df06ba775ea49ad637","last_reissued_at":"2026-07-05T11:14:18.325288Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:14:18.325288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Signature Maximum Mean Discrepancy Two-Sample Statistical Tests","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.DS"],"primary_cat":"stat.ML","authors_text":"Andrew Alden, Blanka Horvath, Zacharia Issa","submitted_at":"2025-06-02T14:26:58Z","abstract_excerpt":"Maximum Mean Discrepancy (MMD) is a widely used concept in machine learning research which has gained popularity in recent years as a highly effective tool for comparing (finite-dimensional) distributions. Since it is designed as a kernel-based method, the MMD can be extended to path space valued distributions using the signature kernel. The resulting signature MMD (sig-MMD) can be used to define a metric between distributions on path space. Similarly to the original use case of the MMD as a test statistic within a two-sample testing framework, the sig-MMD can be applied to determine if two se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01718","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.01718/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.01718","created_at":"2026-07-05T11:14:18.325358+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.01718v1","created_at":"2026-07-05T11:14:18.325358+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01718","created_at":"2026-07-05T11:14:18.325358+00:00"},{"alias_kind":"pith_short_12","alias_value":"PWPJXMT5A6DI","created_at":"2026-07-05T11:14:18.325358+00:00"},{"alias_kind":"pith_short_16","alias_value":"PWPJXMT5A6DI5S7N","created_at":"2026-07-05T11:14:18.325358+00:00"},{"alias_kind":"pith_short_8","alias_value":"PWPJXMT5","created_at":"2026-07-05T11:14:18.325358+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PWPJXMT5A6DI5S7NP32OKTJPYW","json":"https://pith.science/pith/PWPJXMT5A6DI5S7NP32OKTJPYW.json","graph_json":"https://pith.science/api/pith-number/PWPJXMT5A6DI5S7NP32OKTJPYW/graph.json","events_json":"https://pith.science/api/pith-number/PWPJXMT5A6DI5S7NP32OKTJPYW/events.json","paper":"https://pith.science/paper/PWPJXMT5"},"agent_actions":{"view_html":"https://pith.science/pith/PWPJXMT5A6DI5S7NP32OKTJPYW","download_json":"https://pith.science/pith/PWPJXMT5A6DI5S7NP32OKTJPYW.json","view_paper":"https://pith.science/paper/PWPJXMT5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.01718&json=true","fetch_graph":"https://pith.science/api/pith-number/PWPJXMT5A6DI5S7NP32OKTJPYW/graph.json","fetch_events":"https://pith.science/api/pith-number/PWPJXMT5A6DI5S7NP32OKTJPYW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PWPJXMT5A6DI5S7NP32OKTJPYW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PWPJXMT5A6DI5S7NP32OKTJPYW/action/storage_attestation","attest_author":"https://pith.science/pith/PWPJXMT5A6DI5S7NP32OKTJPYW/action/author_attestation","sign_citation":"https://pith.science/pith/PWPJXMT5A6DI5S7NP32OKTJPYW/action/citation_signature","submit_replication":"https://pith.science/pith/PWPJXMT5A6DI5S7NP32OKTJPYW/action/replication_record"}},"created_at":"2026-07-05T11:14:18.325358+00:00","updated_at":"2026-07-05T11:14:18.325358+00:00"}