{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LPU7BFPNFPDW7F6T2PVG5KI7OD","short_pith_number":"pith:LPU7BFPN","canonical_record":{"source":{"id":"1611.00519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-02T09:35:30Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"3885dbd6aa9d6354a4509ab24434ca2df4059cd2fe74bd6cc0419e23ac86290f","abstract_canon_sha256":"a642ceb6bc081827424bd4b3157cc10235a0e179c9455bb6bfffc092f72e1b8e"},"schema_version":"1.0"},"canonical_sha256":"5be9f095ed2bc76f97d3d3ea6ea91f70c12e46f932d2c5eefa29f01d6bceff68","source":{"kind":"arxiv","id":"1611.00519","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00519","created_at":"2026-05-18T00:43:30Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00519v2","created_at":"2026-05-18T00:43:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00519","created_at":"2026-05-18T00:43:30Z"},{"alias_kind":"pith_short_12","alias_value":"LPU7BFPNFPDW","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LPU7BFPNFPDW7F6T","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LPU7BFPN","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LPU7BFPNFPDW7F6T2PVG5KI7OD","target":"record","payload":{"canonical_record":{"source":{"id":"1611.00519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-02T09:35:30Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"3885dbd6aa9d6354a4509ab24434ca2df4059cd2fe74bd6cc0419e23ac86290f","abstract_canon_sha256":"a642ceb6bc081827424bd4b3157cc10235a0e179c9455bb6bfffc092f72e1b8e"},"schema_version":"1.0"},"canonical_sha256":"5be9f095ed2bc76f97d3d3ea6ea91f70c12e46f932d2c5eefa29f01d6bceff68","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:30.097842Z","signature_b64":"Wu8lgkvyttJT5jfkLBrS/9H/+DpXfeJ8YhEDdmBg/ZNytTGEpaJGLByu4SZCvRQKd3476SrlMLm7/W2ZJczcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5be9f095ed2bc76f97d3d3ea6ea91f70c12e46f932d2c5eefa29f01d6bceff68","last_reissued_at":"2026-05-18T00:43:30.097189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:30.097189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.00519","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":"2026-05-18T00:43:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yAqGYs6qSiVBrMjE1ctF45S9gQDcncf32MfNfHe+fq5ZZ2c8Tgawz/M/AsUOU12xAhhSOID907HddxiFueuGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:32:31.892957Z"},"content_sha256":"53cdd7473407482cdc8e05ef7d62cc8768c8a55baa833439ff2e41f5b750bafe","schema_version":"1.0","event_id":"sha256:53cdd7473407482cdc8e05ef7d62cc8768c8a55baa833439ff2e41f5b750bafe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LPU7BFPNFPDW7F6T2PVG5KI7OD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Convergence of the EM Algorithm: A Data-Adaptive Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Can Yang, Chong Wu, Hongyu Zhao, Ji Zhu","submitted_at":"2016-11-02T09:35:30Z","abstract_excerpt":"The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic (population level) convergence rate of the algorithm. In this paper, we give a data-adaptive analysis of the sample level local convergence rate of the EM algorithm. In particular, we show that the local convergence rate of the EM algorithm is a random variable $\\overline{K}_{n}$ derived from the data generating distribution, which adaptively yields the conve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00519","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":"2026-05-18T00:43:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"32Pouwiv87b7eSA9bEEHbO4GwdMCRXoHQXiObJJ49gxIxBueJ7ZiS+PjONwQDmFwwRFH5AQdQeJnT4DXaNyIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:32:31.893743Z"},"content_sha256":"20fe31efff48ad8109c5ee7fd6c08df3f1d5da58e6c37822c8c837269b470f37","schema_version":"1.0","event_id":"sha256:20fe31efff48ad8109c5ee7fd6c08df3f1d5da58e6c37822c8c837269b470f37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LPU7BFPNFPDW7F6T2PVG5KI7OD/bundle.json","state_url":"https://pith.science/pith/LPU7BFPNFPDW7F6T2PVG5KI7OD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LPU7BFPNFPDW7F6T2PVG5KI7OD/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":"2026-08-10T02:32:31Z","links":{"resolver":"https://pith.science/pith/LPU7BFPNFPDW7F6T2PVG5KI7OD","bundle":"https://pith.science/pith/LPU7BFPNFPDW7F6T2PVG5KI7OD/bundle.json","state":"https://pith.science/pith/LPU7BFPNFPDW7F6T2PVG5KI7OD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LPU7BFPNFPDW7F6T2PVG5KI7OD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LPU7BFPNFPDW7F6T2PVG5KI7OD","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":"a642ceb6bc081827424bd4b3157cc10235a0e179c9455bb6bfffc092f72e1b8e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-02T09:35:30Z","title_canon_sha256":"3885dbd6aa9d6354a4509ab24434ca2df4059cd2fe74bd6cc0419e23ac86290f"},"schema_version":"1.0","source":{"id":"1611.00519","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00519","created_at":"2026-05-18T00:43:30Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00519v2","created_at":"2026-05-18T00:43:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00519","created_at":"2026-05-18T00:43:30Z"},{"alias_kind":"pith_short_12","alias_value":"LPU7BFPNFPDW","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LPU7BFPNFPDW7F6T","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LPU7BFPN","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:20fe31efff48ad8109c5ee7fd6c08df3f1d5da58e6c37822c8c837269b470f37","target":"graph","created_at":"2026-05-18T00:43:30Z","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":"The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic (population level) convergence rate of the algorithm. In this paper, we give a data-adaptive analysis of the sample level local convergence rate of the EM algorithm. In particular, we show that the local convergence rate of the EM algorithm is a random variable $\\overline{K}_{n}$ derived from the data generating distribution, which adaptively yields the conve","authors_text":"Can Yang, Chong Wu, Hongyu Zhao, Ji Zhu","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-02T09:35:30Z","title":"On the Convergence of the EM Algorithm: A Data-Adaptive Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00519","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":"sha256:53cdd7473407482cdc8e05ef7d62cc8768c8a55baa833439ff2e41f5b750bafe","target":"record","created_at":"2026-05-18T00:43:30Z","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":"a642ceb6bc081827424bd4b3157cc10235a0e179c9455bb6bfffc092f72e1b8e","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-11-02T09:35:30Z","title_canon_sha256":"3885dbd6aa9d6354a4509ab24434ca2df4059cd2fe74bd6cc0419e23ac86290f"},"schema_version":"1.0","source":{"id":"1611.00519","kind":"arxiv","version":2}},"canonical_sha256":"5be9f095ed2bc76f97d3d3ea6ea91f70c12e46f932d2c5eefa29f01d6bceff68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5be9f095ed2bc76f97d3d3ea6ea91f70c12e46f932d2c5eefa29f01d6bceff68","first_computed_at":"2026-05-18T00:43:30.097189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:30.097189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wu8lgkvyttJT5jfkLBrS/9H/+DpXfeJ8YhEDdmBg/ZNytTGEpaJGLByu4SZCvRQKd3476SrlMLm7/W2ZJczcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:30.097842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.00519","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53cdd7473407482cdc8e05ef7d62cc8768c8a55baa833439ff2e41f5b750bafe","sha256:20fe31efff48ad8109c5ee7fd6c08df3f1d5da58e6c37822c8c837269b470f37"],"state_sha256":"9b880fff3a52e0764508cea300ba96e26263b47b7a6ac23490658880dc220a47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ICJbQ6/TF5if9oStcInygo+d+5xqPsfa7ZdyliRBEmms/PI8B6O9DlQoRIReP/XF5QpwwTNiZr/PYpMMpxODw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T02:32:31.900877Z","bundle_sha256":"4aa08d82ca9377ce779b3ad5de76d9005f1a591a68186eab5aea5f694e583199"}}