{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XI2GEIHSLHUUAMYQAZ2ZWMPRGY","short_pith_number":"pith:XI2GEIHS","schema_version":"1.0","canonical_sha256":"ba346220f259e940331006759b31f13639fb6ee5f5b7ae8d579f65e4444713b3","source":{"kind":"arxiv","id":"1710.11592","version":1},"attestation_state":"computed","paper":{"title":"On Learning Mixtures of Well-Separated Gaussians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Aravindan Vijayaraghavan, Oded Regev","submitted_at":"2017-10-31T17:10:21Z","abstract_excerpt":"We consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. In the most basic form of this problem, we are given samples from a uniform mixture of $k$ standard spherical Gaussians, and the goal is to estimate the means up to accuracy $\\delta$ using $poly(k,d, 1/\\delta)$ samples.\n  In this work, we study the following question: what is the minimum separation needed between the means for solving this task? The best known algorithm due to Vempala and Wang [JCSS 2004] requires a separation of roughly $\\mi"},"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":"1710.11592","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-31T17:10:21Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"084db9c7d8d7f8f69eefe0a871d18c26709cc64153af2dc6f1312e1c1cc9905f","abstract_canon_sha256":"796214ce164fa9d846883735a4fa25c5f0d223e7a26c7e74beb221c327d8c4c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:36.882346Z","signature_b64":"4H1/YCs5hwU+osjx8hY0pdDY6NMptX7+5JnXuQDpXPGbb6icYo5PPtbSMUXcXe/mFUSpOUWMwt+/zAFzvZXbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba346220f259e940331006759b31f13639fb6ee5f5b7ae8d579f65e4444713b3","last_reissued_at":"2026-05-18T00:31:36.881823Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:36.881823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Learning Mixtures of Well-Separated Gaussians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Aravindan Vijayaraghavan, Oded Regev","submitted_at":"2017-10-31T17:10:21Z","abstract_excerpt":"We consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. In the most basic form of this problem, we are given samples from a uniform mixture of $k$ standard spherical Gaussians, and the goal is to estimate the means up to accuracy $\\delta$ using $poly(k,d, 1/\\delta)$ samples.\n  In this work, we study the following question: what is the minimum separation needed between the means for solving this task? The best known algorithm due to Vempala and Wang [JCSS 2004] requires a separation of roughly $\\mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11592","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":"1710.11592","created_at":"2026-05-18T00:31:36.881909+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.11592v1","created_at":"2026-05-18T00:31:36.881909+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11592","created_at":"2026-05-18T00:31:36.881909+00:00"},{"alias_kind":"pith_short_12","alias_value":"XI2GEIHSLHUU","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"XI2GEIHSLHUUAMYQ","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"XI2GEIHS","created_at":"2026-05-18T12:31:53.515858+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/XI2GEIHSLHUUAMYQAZ2ZWMPRGY","json":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY.json","graph_json":"https://pith.science/api/pith-number/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/graph.json","events_json":"https://pith.science/api/pith-number/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/events.json","paper":"https://pith.science/paper/XI2GEIHS"},"agent_actions":{"view_html":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY","download_json":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY.json","view_paper":"https://pith.science/paper/XI2GEIHS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.11592&json=true","fetch_graph":"https://pith.science/api/pith-number/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/graph.json","fetch_events":"https://pith.science/api/pith-number/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/action/storage_attestation","attest_author":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/action/author_attestation","sign_citation":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/action/citation_signature","submit_replication":"https://pith.science/pith/XI2GEIHSLHUUAMYQAZ2ZWMPRGY/action/replication_record"}},"created_at":"2026-05-18T00:31:36.881909+00:00","updated_at":"2026-05-18T00:31:36.881909+00:00"}