{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UKLZEKNE25L54G27MMWI655NAR","short_pith_number":"pith:UKLZEKNE","canonical_record":{"source":{"id":"1512.08269","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-12-27T20:10:20Z","cross_cats_sorted":["cs.IT","math.IT","math.ST","stat.TH"],"title_canon_sha256":"ff1d177eb5d2d8817d6aff3398df1bd23842b98e5b26b129e5106384b06e71b9","abstract_canon_sha256":"45a306049d64c9b14dcf32b686a12810a0c2deac37f83505e163d72c60ee2833"},"schema_version":"1.0"},"canonical_sha256":"a2979229a4d757de1b5f632c8f77ad04658182bc95e2fba8d88487d4f7acf917","source":{"kind":"arxiv","id":"1512.08269","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08269","created_at":"2026-05-18T01:23:42Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08269v1","created_at":"2026-05-18T01:23:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08269","created_at":"2026-05-18T01:23:42Z"},{"alias_kind":"pith_short_12","alias_value":"UKLZEKNE25L5","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UKLZEKNE25L54G27","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UKLZEKNE","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UKLZEKNE25L54G27MMWI655NAR","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08269","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-12-27T20:10:20Z","cross_cats_sorted":["cs.IT","math.IT","math.ST","stat.TH"],"title_canon_sha256":"ff1d177eb5d2d8817d6aff3398df1bd23842b98e5b26b129e5106384b06e71b9","abstract_canon_sha256":"45a306049d64c9b14dcf32b686a12810a0c2deac37f83505e163d72c60ee2833"},"schema_version":"1.0"},"canonical_sha256":"a2979229a4d757de1b5f632c8f77ad04658182bc95e2fba8d88487d4f7acf917","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:42.744771Z","signature_b64":"8VrkoVnfADB8RlwK84WTYYsZGMbj2KOs80wR2+TNiSIHqlJ5mDAv68/hvOKVCA9B1PEysKFesYU2p0V+nXUGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2979229a4d757de1b5f632c8f77ad04658182bc95e2fba8d88487d4f7acf917","last_reissued_at":"2026-05-18T01:23:42.744058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:42.744058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08269","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J6M0fMNwXCUHLE3Q0o2Ya+cAZBYuq7pTRABn4oPw7/OJfg0jCib57XJhS0HjAiMajJHwExpgWbRyEE8HtWyOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:38:01.433478Z"},"content_sha256":"31c537e9eaea47bd569cb977bd683febe97e55fae263c75d91c6bbcdc2751d98","schema_version":"1.0","event_id":"sha256:31c537e9eaea47bd569cb977bd683febe97e55fae263c75d91c6bbcdc2751d98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UKLZEKNE25L54G27MMWI655NAR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical and Computational Guarantees for the Baum-Welch Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Fanny Yang, Martin J. Wainwright, Sivaraman Balakrishnan","submitted_at":"2015-12-27T20:10:20Z","abstract_excerpt":"The Hidden Markov Model (HMM) is one of the mainstays of statistical modeling of discrete time series, with applications including speech recognition, computational biology, computer vision and econometrics. Estimating an HMM from its observation process is often addressed via the Baum-Welch algorithm, which is known to be susceptible to local optima. In this paper, we first give a general characterization of the basin of attraction associated with any global optimum of the population likelihood. By exploiting this characterization, we provide non-asymptotic finite sample guarantees on the Bau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08269","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"okOX700kAd8o3uWtetSj60enSVMl6qBMX6KEmYf2rFurPb5yZyZaRk1Eco0DjKphpStTONx9tjjzDWbfgHrKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:38:01.434157Z"},"content_sha256":"12d8588f16dff87df896eeb3175f619159b3a4c179727b39c55338c4ac0d26ca","schema_version":"1.0","event_id":"sha256:12d8588f16dff87df896eeb3175f619159b3a4c179727b39c55338c4ac0d26ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UKLZEKNE25L54G27MMWI655NAR/bundle.json","state_url":"https://pith.science/pith/UKLZEKNE25L54G27MMWI655NAR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UKLZEKNE25L54G27MMWI655NAR/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":"2026-05-26T03:38:01Z","links":{"resolver":"https://pith.science/pith/UKLZEKNE25L54G27MMWI655NAR","bundle":"https://pith.science/pith/UKLZEKNE25L54G27MMWI655NAR/bundle.json","state":"https://pith.science/pith/UKLZEKNE25L54G27MMWI655NAR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UKLZEKNE25L54G27MMWI655NAR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UKLZEKNE25L54G27MMWI655NAR","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":"45a306049d64c9b14dcf32b686a12810a0c2deac37f83505e163d72c60ee2833","cross_cats_sorted":["cs.IT","math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-12-27T20:10:20Z","title_canon_sha256":"ff1d177eb5d2d8817d6aff3398df1bd23842b98e5b26b129e5106384b06e71b9"},"schema_version":"1.0","source":{"id":"1512.08269","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08269","created_at":"2026-05-18T01:23:42Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08269v1","created_at":"2026-05-18T01:23:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08269","created_at":"2026-05-18T01:23:42Z"},{"alias_kind":"pith_short_12","alias_value":"UKLZEKNE25L5","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UKLZEKNE25L54G27","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UKLZEKNE","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:12d8588f16dff87df896eeb3175f619159b3a4c179727b39c55338c4ac0d26ca","target":"graph","created_at":"2026-05-18T01:23:42Z","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 Hidden Markov Model (HMM) is one of the mainstays of statistical modeling of discrete time series, with applications including speech recognition, computational biology, computer vision and econometrics. Estimating an HMM from its observation process is often addressed via the Baum-Welch algorithm, which is known to be susceptible to local optima. In this paper, we first give a general characterization of the basin of attraction associated with any global optimum of the population likelihood. By exploiting this characterization, we provide non-asymptotic finite sample guarantees on the Bau","authors_text":"Fanny Yang, Martin J. Wainwright, Sivaraman Balakrishnan","cross_cats":["cs.IT","math.IT","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-12-27T20:10:20Z","title":"Statistical and Computational Guarantees for the Baum-Welch Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08269","kind":"arxiv","version":1},"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":"sha256:31c537e9eaea47bd569cb977bd683febe97e55fae263c75d91c6bbcdc2751d98","target":"record","created_at":"2026-05-18T01:23:42Z","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":"45a306049d64c9b14dcf32b686a12810a0c2deac37f83505e163d72c60ee2833","cross_cats_sorted":["cs.IT","math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-12-27T20:10:20Z","title_canon_sha256":"ff1d177eb5d2d8817d6aff3398df1bd23842b98e5b26b129e5106384b06e71b9"},"schema_version":"1.0","source":{"id":"1512.08269","kind":"arxiv","version":1}},"canonical_sha256":"a2979229a4d757de1b5f632c8f77ad04658182bc95e2fba8d88487d4f7acf917","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2979229a4d757de1b5f632c8f77ad04658182bc95e2fba8d88487d4f7acf917","first_computed_at":"2026-05-18T01:23:42.744058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:42.744058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8VrkoVnfADB8RlwK84WTYYsZGMbj2KOs80wR2+TNiSIHqlJ5mDAv68/hvOKVCA9B1PEysKFesYU2p0V+nXUGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:42.744771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08269","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31c537e9eaea47bd569cb977bd683febe97e55fae263c75d91c6bbcdc2751d98","sha256:12d8588f16dff87df896eeb3175f619159b3a4c179727b39c55338c4ac0d26ca"],"state_sha256":"a4da226020abf5db927f1de4d2c01b09c7be4596edb61eac32c2085dc0eacd45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OBjAqCulUSDtJohFIdHUG4RRy6rIsrbgmbhwyJ5XhiEpuBQ1lfgRzRk01tk0s/dsF2fngf/fUuO4d+6kLWrwAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:38:01.437458Z","bundle_sha256":"a9cb7d2863283b54b6988246f9ae76052fce9a9d355aa2e7b0cff94bcdd1b9ac"}}