{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:KBHGJ5DTAWLPTA6Z56JBO5WH3G","short_pith_number":"pith:KBHGJ5DT","schema_version":"1.0","canonical_sha256":"504e64f4730596f983d9ef921776c7d9bf5864ee639c666c3e8705970767713f","source":{"kind":"arxiv","id":"2002.09073","version":3},"attestation_state":"computed","paper":{"title":"Improved guarantees and a multiple-descent curve for Column Subset Selection and the Nystr\\\"om method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Michael W. Mahoney, Micha{\\l} Derezi\\'nski, Rajiv Khanna","submitted_at":"2020-02-21T00:43:06Z","abstract_excerpt":"The Column Subset Selection Problem (CSSP) and the Nystr\\\"om method are among the leading tools for constructing small low-rank approximations of large datasets in machine learning and scientific computing. A fundamental question in this area is: how well can a data subset of size k compete with the best rank k approximation? We develop techniques which exploit spectral properties of the data matrix to obtain improved approximation guarantees which go beyond the standard worst-case analysis. Our approach leads to significantly better bounds for datasets with known rates of singular value decay"},"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":"2002.09073","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-02-21T00:43:06Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"d49f3e14a4b4204a8534450457eb0b4ac66e6e7b8687567c65b8967e11650a02","abstract_canon_sha256":"7d723674ee8592ba12c6d8ec446bcc2d6e08e3a86fb25cff787908ac12140535"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:00:43.862541Z","signature_b64":"Os2zhGsgbLOZ0ZH4i9GKuE2oeU1DyNOn9CXnF/UwLZ2edLBVGGRbubZbAtaN8+paazSjdkKcW7sGC9AC9H+9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"504e64f4730596f983d9ef921776c7d9bf5864ee639c666c3e8705970767713f","last_reissued_at":"2026-07-05T02:00:43.862148Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:00:43.862148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved guarantees and a multiple-descent curve for Column Subset Selection and the Nystr\\\"om method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Michael W. Mahoney, Micha{\\l} Derezi\\'nski, Rajiv Khanna","submitted_at":"2020-02-21T00:43:06Z","abstract_excerpt":"The Column Subset Selection Problem (CSSP) and the Nystr\\\"om method are among the leading tools for constructing small low-rank approximations of large datasets in machine learning and scientific computing. A fundamental question in this area is: how well can a data subset of size k compete with the best rank k approximation? We develop techniques which exploit spectral properties of the data matrix to obtain improved approximation guarantees which go beyond the standard worst-case analysis. Our approach leads to significantly better bounds for datasets with known rates of singular value decay"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.09073","kind":"arxiv","version":3},"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/2002.09073/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":"2002.09073","created_at":"2026-07-05T02:00:43.862209+00:00"},{"alias_kind":"arxiv_version","alias_value":"2002.09073v3","created_at":"2026-07-05T02:00:43.862209+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.09073","created_at":"2026-07-05T02:00:43.862209+00:00"},{"alias_kind":"pith_short_12","alias_value":"KBHGJ5DTAWLP","created_at":"2026-07-05T02:00:43.862209+00:00"},{"alias_kind":"pith_short_16","alias_value":"KBHGJ5DTAWLPTA6Z","created_at":"2026-07-05T02:00:43.862209+00:00"},{"alias_kind":"pith_short_8","alias_value":"KBHGJ5DT","created_at":"2026-07-05T02:00:43.862209+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.08101","citing_title":"Perturbations of CUR Decompositions","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KBHGJ5DTAWLPTA6Z56JBO5WH3G","json":"https://pith.science/pith/KBHGJ5DTAWLPTA6Z56JBO5WH3G.json","graph_json":"https://pith.science/api/pith-number/KBHGJ5DTAWLPTA6Z56JBO5WH3G/graph.json","events_json":"https://pith.science/api/pith-number/KBHGJ5DTAWLPTA6Z56JBO5WH3G/events.json","paper":"https://pith.science/paper/KBHGJ5DT"},"agent_actions":{"view_html":"https://pith.science/pith/KBHGJ5DTAWLPTA6Z56JBO5WH3G","download_json":"https://pith.science/pith/KBHGJ5DTAWLPTA6Z56JBO5WH3G.json","view_paper":"https://pith.science/paper/KBHGJ5DT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2002.09073&json=true","fetch_graph":"https://pith.science/api/pith-number/KBHGJ5DTAWLPTA6Z56JBO5WH3G/graph.json","fetch_events":"https://pith.science/api/pith-number/KBHGJ5DTAWLPTA6Z56JBO5WH3G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KBHGJ5DTAWLPTA6Z56JBO5WH3G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KBHGJ5DTAWLPTA6Z56JBO5WH3G/action/storage_attestation","attest_author":"https://pith.science/pith/KBHGJ5DTAWLPTA6Z56JBO5WH3G/action/author_attestation","sign_citation":"https://pith.science/pith/KBHGJ5DTAWLPTA6Z56JBO5WH3G/action/citation_signature","submit_replication":"https://pith.science/pith/KBHGJ5DTAWLPTA6Z56JBO5WH3G/action/replication_record"}},"created_at":"2026-07-05T02:00:43.862209+00:00","updated_at":"2026-07-05T02:00:43.862209+00:00"}