{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:UOTANYLC6KVYP5W6TZT2SHYJI7","short_pith_number":"pith:UOTANYLC","schema_version":"1.0","canonical_sha256":"a3a606e162f2ab87f6de9e67a91f0947ffa3e934ffc5414465b0650b1698ebe2","source":{"kind":"arxiv","id":"1406.5752","version":1},"attestation_state":"computed","paper":{"title":"Divide-and-Conquer Learning by Anchoring a Conical Hull","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Carlos Guestrin, Jeff Bilmes, Tianyi Zhou","submitted_at":"2014-06-22T19:16:20Z","abstract_excerpt":"We reduce a broad class of machine learning problems, usually addressed by EM or sampling, to the problem of finding the $k$ extremal rays spanning the conical hull of a data point set. These $k$ \"anchors\" lead to a global solution and a more interpretable model that can even outperform EM and sampling on generalization error. To find the $k$ anchors, we propose a novel divide-and-conquer learning scheme \"DCA\" that distributes the problem to $\\mathcal O(k\\log k)$ same-type sub-problems on different low-D random hyperplanes, each can be solved by any solver. For the 2D sub-problem, we present a"},"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":"1406.5752","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"stat.ML","submitted_at":"2014-06-22T19:16:20Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"b0c647cf4a48ee6ae4a20740ab6aa601754affe218242565e459df4e99ce9603","abstract_canon_sha256":"ee812a7c49ed195d9beba9aa00fa59e5a122db1493d55c4c9b19f7c7ad596874"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:10.815187Z","signature_b64":"cL3Rre1nghg5I1hT2zFVo01F6rhxDFwLhbtznS5bbE5v8oOxtel5PJyOYaMa1xGwpOOdOMuoPj/8BdxWjjXPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3a606e162f2ab87f6de9e67a91f0947ffa3e934ffc5414465b0650b1698ebe2","last_reissued_at":"2026-05-18T02:49:10.814805Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:10.814805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Divide-and-Conquer Learning by Anchoring a Conical Hull","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Carlos Guestrin, Jeff Bilmes, Tianyi Zhou","submitted_at":"2014-06-22T19:16:20Z","abstract_excerpt":"We reduce a broad class of machine learning problems, usually addressed by EM or sampling, to the problem of finding the $k$ extremal rays spanning the conical hull of a data point set. These $k$ \"anchors\" lead to a global solution and a more interpretable model that can even outperform EM and sampling on generalization error. To find the $k$ anchors, we propose a novel divide-and-conquer learning scheme \"DCA\" that distributes the problem to $\\mathcal O(k\\log k)$ same-type sub-problems on different low-D random hyperplanes, each can be solved by any solver. For the 2D sub-problem, we present a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5752","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":""},"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":"1406.5752","created_at":"2026-05-18T02:49:10.814863+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.5752v1","created_at":"2026-05-18T02:49:10.814863+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5752","created_at":"2026-05-18T02:49:10.814863+00:00"},{"alias_kind":"pith_short_12","alias_value":"UOTANYLC6KVY","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UOTANYLC6KVYP5W6","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UOTANYLC","created_at":"2026-05-18T12:28:52.271510+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/UOTANYLC6KVYP5W6TZT2SHYJI7","json":"https://pith.science/pith/UOTANYLC6KVYP5W6TZT2SHYJI7.json","graph_json":"https://pith.science/api/pith-number/UOTANYLC6KVYP5W6TZT2SHYJI7/graph.json","events_json":"https://pith.science/api/pith-number/UOTANYLC6KVYP5W6TZT2SHYJI7/events.json","paper":"https://pith.science/paper/UOTANYLC"},"agent_actions":{"view_html":"https://pith.science/pith/UOTANYLC6KVYP5W6TZT2SHYJI7","download_json":"https://pith.science/pith/UOTANYLC6KVYP5W6TZT2SHYJI7.json","view_paper":"https://pith.science/paper/UOTANYLC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.5752&json=true","fetch_graph":"https://pith.science/api/pith-number/UOTANYLC6KVYP5W6TZT2SHYJI7/graph.json","fetch_events":"https://pith.science/api/pith-number/UOTANYLC6KVYP5W6TZT2SHYJI7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UOTANYLC6KVYP5W6TZT2SHYJI7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UOTANYLC6KVYP5W6TZT2SHYJI7/action/storage_attestation","attest_author":"https://pith.science/pith/UOTANYLC6KVYP5W6TZT2SHYJI7/action/author_attestation","sign_citation":"https://pith.science/pith/UOTANYLC6KVYP5W6TZT2SHYJI7/action/citation_signature","submit_replication":"https://pith.science/pith/UOTANYLC6KVYP5W6TZT2SHYJI7/action/replication_record"}},"created_at":"2026-05-18T02:49:10.814863+00:00","updated_at":"2026-05-18T02:49:10.814863+00:00"}