{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SOISH7NXNNO2CSSJP65KR5FKAD","short_pith_number":"pith:SOISH7NX","canonical_record":{"source":{"id":"1705.08530","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-23T20:47:17Z","cross_cats_sorted":["cs.LG","stat.TH"],"title_canon_sha256":"b8dfa38780a2fc5ebb206fcc5e9c06549435d6c54cefdefbaf107dd136404cbf","abstract_canon_sha256":"532d2265a0451d2f383840977536f344870f62cefef12289b61e47e05cfd18b1"},"schema_version":"1.0"},"canonical_sha256":"939123fdb76b5da14a497fbaa8f4aa00d7a9bd9106b6db90a472d13772fbaca4","source":{"kind":"arxiv","id":"1705.08530","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08530","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08530v2","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08530","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"SOISH7NXNNO2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SOISH7NXNNO2CSSJ","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SOISH7NX","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SOISH7NXNNO2CSSJP65KR5FKAD","target":"record","payload":{"canonical_record":{"source":{"id":"1705.08530","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-23T20:47:17Z","cross_cats_sorted":["cs.LG","stat.TH"],"title_canon_sha256":"b8dfa38780a2fc5ebb206fcc5e9c06549435d6c54cefdefbaf107dd136404cbf","abstract_canon_sha256":"532d2265a0451d2f383840977536f344870f62cefef12289b61e47e05cfd18b1"},"schema_version":"1.0"},"canonical_sha256":"939123fdb76b5da14a497fbaa8f4aa00d7a9bd9106b6db90a472d13772fbaca4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:01.505230Z","signature_b64":"dtLHpLn3vszZgJzb+rDX5HM/GBhysHv0uLW/2EMwDAjgXaIHyMdxgVPCYTIHYBvpDtkeQlDFIYokFaMrnltJDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"939123fdb76b5da14a497fbaa8f4aa00d7a9bd9106b6db90a472d13772fbaca4","last_reissued_at":"2026-05-18T00:29:01.504827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:01.504827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.08530","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ciLM5rJrBNc1MtBnBmykNfE5c/2dd+JEhy9+UAzhPcH3TV12k0HjtLjMpH4FNtVKuWLNdtUtF4eoudsf84SpCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:36:58.461700Z"},"content_sha256":"1004a210096144aed9d6c0836fe81f61c96db2b7e362055fea4f2c4976a07133","schema_version":"1.0","event_id":"sha256:1004a210096144aed9d6c0836fe81f61c96db2b7e362055fea4f2c4976a07133"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SOISH7NXNNO2CSSJP65KR5FKAD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence Analysis of Gradient EM for Multi-component Gaussian Mixture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.TH"],"primary_cat":"math.ST","authors_text":"Bowei Yan, Mingzhang Yin, Purnamrita Sarkar","submitted_at":"2017-05-23T20:47:17Z","abstract_excerpt":"In this paper, we study convergence properties of the gradient Expectation-Maximization algorithm \\cite{lange1995gradient} for Gaussian Mixture Models for general number of clusters and mixing coefficients. We derive the convergence rate depending on the mixing coefficients, minimum and maximum pairwise distances between the true centers and dimensionality and number of components; and obtain a near-optimal local contraction radius. While there have been some recent notable works that derive local convergence rates for EM in the two equal mixture symmetric GMM, in the more general case, the de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08530","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l1ELuGzxvHmRuaVfiTW8+GjTlOAAYivaBj9D2S1ZDzMfyTOmlQc1s756dXfd1nlRCcqYqzEDpxPAVhJFcEdjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:36:58.462076Z"},"content_sha256":"a599dc362b3d71f66f4aaa7da02c1d7b494ed0f46ec21ec586381ee31add50d6","schema_version":"1.0","event_id":"sha256:a599dc362b3d71f66f4aaa7da02c1d7b494ed0f46ec21ec586381ee31add50d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SOISH7NXNNO2CSSJP65KR5FKAD/bundle.json","state_url":"https://pith.science/pith/SOISH7NXNNO2CSSJP65KR5FKAD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SOISH7NXNNO2CSSJP65KR5FKAD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T02:36:58Z","links":{"resolver":"https://pith.science/pith/SOISH7NXNNO2CSSJP65KR5FKAD","bundle":"https://pith.science/pith/SOISH7NXNNO2CSSJP65KR5FKAD/bundle.json","state":"https://pith.science/pith/SOISH7NXNNO2CSSJP65KR5FKAD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SOISH7NXNNO2CSSJP65KR5FKAD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SOISH7NXNNO2CSSJP65KR5FKAD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"532d2265a0451d2f383840977536f344870f62cefef12289b61e47e05cfd18b1","cross_cats_sorted":["cs.LG","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-23T20:47:17Z","title_canon_sha256":"b8dfa38780a2fc5ebb206fcc5e9c06549435d6c54cefdefbaf107dd136404cbf"},"schema_version":"1.0","source":{"id":"1705.08530","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08530","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08530v2","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08530","created_at":"2026-05-18T00:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"SOISH7NXNNO2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SOISH7NXNNO2CSSJ","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SOISH7NX","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:a599dc362b3d71f66f4aaa7da02c1d7b494ed0f46ec21ec586381ee31add50d6","target":"graph","created_at":"2026-05-18T00:29:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we study convergence properties of the gradient Expectation-Maximization algorithm \\cite{lange1995gradient} for Gaussian Mixture Models for general number of clusters and mixing coefficients. We derive the convergence rate depending on the mixing coefficients, minimum and maximum pairwise distances between the true centers and dimensionality and number of components; and obtain a near-optimal local contraction radius. While there have been some recent notable works that derive local convergence rates for EM in the two equal mixture symmetric GMM, in the more general case, the de","authors_text":"Bowei Yan, Mingzhang Yin, Purnamrita Sarkar","cross_cats":["cs.LG","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-23T20:47:17Z","title":"Convergence Analysis of Gradient EM for Multi-component Gaussian Mixture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08530","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1004a210096144aed9d6c0836fe81f61c96db2b7e362055fea4f2c4976a07133","target":"record","created_at":"2026-05-18T00:29:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"532d2265a0451d2f383840977536f344870f62cefef12289b61e47e05cfd18b1","cross_cats_sorted":["cs.LG","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-23T20:47:17Z","title_canon_sha256":"b8dfa38780a2fc5ebb206fcc5e9c06549435d6c54cefdefbaf107dd136404cbf"},"schema_version":"1.0","source":{"id":"1705.08530","kind":"arxiv","version":2}},"canonical_sha256":"939123fdb76b5da14a497fbaa8f4aa00d7a9bd9106b6db90a472d13772fbaca4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"939123fdb76b5da14a497fbaa8f4aa00d7a9bd9106b6db90a472d13772fbaca4","first_computed_at":"2026-05-18T00:29:01.504827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:01.504827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dtLHpLn3vszZgJzb+rDX5HM/GBhysHv0uLW/2EMwDAjgXaIHyMdxgVPCYTIHYBvpDtkeQlDFIYokFaMrnltJDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:01.505230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08530","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1004a210096144aed9d6c0836fe81f61c96db2b7e362055fea4f2c4976a07133","sha256:a599dc362b3d71f66f4aaa7da02c1d7b494ed0f46ec21ec586381ee31add50d6"],"state_sha256":"4c32fed97bdfff6f63f0d1cb295bf759922d19af202852f777b0995e49c1cb51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gEl9VI2cKSauBpyrWIrtHxA6U5+bh6cuH3Kv1VGsntyXNzxCnK4D8eKdyR55/QOHDOaZqlI2UCKFB1SdBTDJBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:36:58.464478Z","bundle_sha256":"45e58e9b3e551018bd984a72370b98ca506d277a5ffd5ae2049f6ad016d60e88"}}