{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:J7YCB5IKHMB3ULFNMMMP4X7LYX","short_pith_number":"pith:J7YCB5IK","schema_version":"1.0","canonical_sha256":"4ff020f50a3b03ba2cad6318fe5febc5dba1b8b4d9d5148d43936b2cf0880fb3","source":{"kind":"arxiv","id":"1901.08949","version":5},"attestation_state":"computed","paper":{"title":"Subspace Robust Wasserstein Distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Fran\\c{c}ois-Pierre Paty, Marco Cuturi","submitted_at":"2019-01-25T16:10:02Z","abstract_excerpt":"Making sense of Wasserstein distances between discrete measures in high-dimensional settings remains a challenge. Recent work has advocated a two-step approach to improve robustness and facilitate the computation of optimal transport, using for instance projections on random real lines, or a preliminary quantization of the measures to reduce the size of their support. We propose in this work a \"max-min\" robust variant of the Wasserstein distance by considering the maximal possible distance that can be realized between two measures, assuming they can be projected orthogonally on a lower $k$-dim"},"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":"1901.08949","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-01-25T16:10:02Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3ef9fec580eefc12aea63179ae6ab2d15fa5613d2dee07e212a9676859ee200d","abstract_canon_sha256":"654bc2b4658f2130527425ef19d39f6282b6bbf95a004390952b5cceac8859d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:00:55.164029Z","signature_b64":"jhm6Lgbi9k4FPhXoT5Bz63ULNji2c/el0LFpKQfhm1zKH5eTH+TnJ81mVEtUnXjTaZUNiDxTFSkD95Zp0OMzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ff020f50a3b03ba2cad6318fe5febc5dba1b8b4d9d5148d43936b2cf0880fb3","last_reissued_at":"2026-07-05T00:00:55.163564Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:00:55.163564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subspace Robust Wasserstein Distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Fran\\c{c}ois-Pierre Paty, Marco Cuturi","submitted_at":"2019-01-25T16:10:02Z","abstract_excerpt":"Making sense of Wasserstein distances between discrete measures in high-dimensional settings remains a challenge. Recent work has advocated a two-step approach to improve robustness and facilitate the computation of optimal transport, using for instance projections on random real lines, or a preliminary quantization of the measures to reduce the size of their support. We propose in this work a \"max-min\" robust variant of the Wasserstein distance by considering the maximal possible distance that can be realized between two measures, assuming they can be projected orthogonally on a lower $k$-dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08949","kind":"arxiv","version":5},"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/1901.08949/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":"1901.08949","created_at":"2026-07-05T00:00:55.163623+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.08949v5","created_at":"2026-07-05T00:00:55.163623+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.08949","created_at":"2026-07-05T00:00:55.163623+00:00"},{"alias_kind":"pith_short_12","alias_value":"J7YCB5IKHMB3","created_at":"2026-07-05T00:00:55.163623+00:00"},{"alias_kind":"pith_short_16","alias_value":"J7YCB5IKHMB3ULFN","created_at":"2026-07-05T00:00:55.163623+00:00"},{"alias_kind":"pith_short_8","alias_value":"J7YCB5IK","created_at":"2026-07-05T00:00:55.163623+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/J7YCB5IKHMB3ULFNMMMP4X7LYX","json":"https://pith.science/pith/J7YCB5IKHMB3ULFNMMMP4X7LYX.json","graph_json":"https://pith.science/api/pith-number/J7YCB5IKHMB3ULFNMMMP4X7LYX/graph.json","events_json":"https://pith.science/api/pith-number/J7YCB5IKHMB3ULFNMMMP4X7LYX/events.json","paper":"https://pith.science/paper/J7YCB5IK"},"agent_actions":{"view_html":"https://pith.science/pith/J7YCB5IKHMB3ULFNMMMP4X7LYX","download_json":"https://pith.science/pith/J7YCB5IKHMB3ULFNMMMP4X7LYX.json","view_paper":"https://pith.science/paper/J7YCB5IK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.08949&json=true","fetch_graph":"https://pith.science/api/pith-number/J7YCB5IKHMB3ULFNMMMP4X7LYX/graph.json","fetch_events":"https://pith.science/api/pith-number/J7YCB5IKHMB3ULFNMMMP4X7LYX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J7YCB5IKHMB3ULFNMMMP4X7LYX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J7YCB5IKHMB3ULFNMMMP4X7LYX/action/storage_attestation","attest_author":"https://pith.science/pith/J7YCB5IKHMB3ULFNMMMP4X7LYX/action/author_attestation","sign_citation":"https://pith.science/pith/J7YCB5IKHMB3ULFNMMMP4X7LYX/action/citation_signature","submit_replication":"https://pith.science/pith/J7YCB5IKHMB3ULFNMMMP4X7LYX/action/replication_record"}},"created_at":"2026-07-05T00:00:55.163623+00:00","updated_at":"2026-07-05T00:00:55.163623+00:00"}