{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:RDUWLDBDI4CS7PHQLUMEJLHLOQ","short_pith_number":"pith:RDUWLDBD","schema_version":"1.0","canonical_sha256":"88e9658c2347052fbcf05d1844aceb740fc342ae2ae614519dee72c58285a011","source":{"kind":"arxiv","id":"1211.2227","version":3},"attestation_state":"computed","paper":{"title":"Efficient learning of simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Joseph Anderson, Luis Rademacher, Navin Goyal","submitted_at":"2012-11-09T20:47:23Z","abstract_excerpt":"We show an efficient algorithm for the following problem: Given uniformly random points from an arbitrary n-dimensional simplex, estimate the simplex. The size of the sample and the number of arithmetic operations of our algorithm are polynomial in n. This answers a question of Frieze, Jerrum and Kannan [FJK]. Our result can also be interpreted as efficiently learning the intersection of n+1 half-spaces in R^n in the model where the intersection is bounded and we are given polynomially many uniform samples from it. Our proof uses the local search technique from Independent Component Analysis ("},"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":"1211.2227","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-11-09T20:47:23Z","cross_cats_sorted":["cs.DS","stat.ML"],"title_canon_sha256":"5105a5451755eb9277bd5e4dc330727a51b69721464e9370d1d02177e19afa7d","abstract_canon_sha256":"967dc99bb45be2f03cd7c08d586cfbce4d69c79b2539bec0986ed2617639dbcf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:43.503255Z","signature_b64":"duHmLxgdiCStb3GsvradHYY628JXyiPtStJvMt2hCtvo3VGbCJGbBWzbevStsbLHiAnvtstPjDYuFCbEjuE4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88e9658c2347052fbcf05d1844aceb740fc342ae2ae614519dee72c58285a011","last_reissued_at":"2026-05-18T03:21:43.502753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:43.502753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient learning of simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Joseph Anderson, Luis Rademacher, Navin Goyal","submitted_at":"2012-11-09T20:47:23Z","abstract_excerpt":"We show an efficient algorithm for the following problem: Given uniformly random points from an arbitrary n-dimensional simplex, estimate the simplex. The size of the sample and the number of arithmetic operations of our algorithm are polynomial in n. This answers a question of Frieze, Jerrum and Kannan [FJK]. Our result can also be interpreted as efficiently learning the intersection of n+1 half-spaces in R^n in the model where the intersection is bounded and we are given polynomially many uniform samples from it. Our proof uses the local search technique from Independent Component Analysis ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2227","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":""},"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":"1211.2227","created_at":"2026-05-18T03:21:43.502828+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.2227v3","created_at":"2026-05-18T03:21:43.502828+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2227","created_at":"2026-05-18T03:21:43.502828+00:00"},{"alias_kind":"pith_short_12","alias_value":"RDUWLDBDI4CS","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"RDUWLDBDI4CS7PHQ","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"RDUWLDBD","created_at":"2026-05-18T12:27:20.899486+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/RDUWLDBDI4CS7PHQLUMEJLHLOQ","json":"https://pith.science/pith/RDUWLDBDI4CS7PHQLUMEJLHLOQ.json","graph_json":"https://pith.science/api/pith-number/RDUWLDBDI4CS7PHQLUMEJLHLOQ/graph.json","events_json":"https://pith.science/api/pith-number/RDUWLDBDI4CS7PHQLUMEJLHLOQ/events.json","paper":"https://pith.science/paper/RDUWLDBD"},"agent_actions":{"view_html":"https://pith.science/pith/RDUWLDBDI4CS7PHQLUMEJLHLOQ","download_json":"https://pith.science/pith/RDUWLDBDI4CS7PHQLUMEJLHLOQ.json","view_paper":"https://pith.science/paper/RDUWLDBD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.2227&json=true","fetch_graph":"https://pith.science/api/pith-number/RDUWLDBDI4CS7PHQLUMEJLHLOQ/graph.json","fetch_events":"https://pith.science/api/pith-number/RDUWLDBDI4CS7PHQLUMEJLHLOQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RDUWLDBDI4CS7PHQLUMEJLHLOQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RDUWLDBDI4CS7PHQLUMEJLHLOQ/action/storage_attestation","attest_author":"https://pith.science/pith/RDUWLDBDI4CS7PHQLUMEJLHLOQ/action/author_attestation","sign_citation":"https://pith.science/pith/RDUWLDBDI4CS7PHQLUMEJLHLOQ/action/citation_signature","submit_replication":"https://pith.science/pith/RDUWLDBDI4CS7PHQLUMEJLHLOQ/action/replication_record"}},"created_at":"2026-05-18T03:21:43.502828+00:00","updated_at":"2026-05-18T03:21:43.502828+00:00"}