{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FYSKFWMN656RX56AKV4VWJN5HN","short_pith_number":"pith:FYSKFWMN","canonical_record":{"source":{"id":"1401.6276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-01-24T07:50:28Z","cross_cats_sorted":[],"title_canon_sha256":"8a7bf41ce5a9bd212b7eb1f4cb8e94ff0ccd0a1cbe0a66a2fbf606d899f5af53","abstract_canon_sha256":"04afd8ed1d2747f74162d14904f962e08929dd8958ef839dd94fc97dc1174631"},"schema_version":"1.0"},"canonical_sha256":"2e24a2d98df77d1bf7c055795b25bd3b4dcd3919d07db3ac0ad98e311c7cfd67","source":{"kind":"arxiv","id":"1401.6276","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6276","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6276v1","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6276","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"pith_short_12","alias_value":"FYSKFWMN656R","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FYSKFWMN656RX56A","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FYSKFWMN","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FYSKFWMN656RX56AKV4VWJN5HN","target":"record","payload":{"canonical_record":{"source":{"id":"1401.6276","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-01-24T07:50:28Z","cross_cats_sorted":[],"title_canon_sha256":"8a7bf41ce5a9bd212b7eb1f4cb8e94ff0ccd0a1cbe0a66a2fbf606d899f5af53","abstract_canon_sha256":"04afd8ed1d2747f74162d14904f962e08929dd8958ef839dd94fc97dc1174631"},"schema_version":"1.0"},"canonical_sha256":"2e24a2d98df77d1bf7c055795b25bd3b4dcd3919d07db3ac0ad98e311c7cfd67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:12.614942Z","signature_b64":"LBJDu5L2TmaNzzmDshsWWzg9Qba8sjo8PjpkzBxuzN/GwXQqWBWk4gYiEXZf0WiEQob87TT68r6WscG7Jc6iCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e24a2d98df77d1bf7c055795b25bd3b4dcd3919d07db3ac0ad98e311c7cfd67","last_reissued_at":"2026-05-18T03:01:12.614194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:12.614194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.6276","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":"2026-05-18T03:01:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pK/ZWM2IpQ6mjsfAeVwyGq9RvurhM6YfD7tDMm7pe3r3rc4B97Oks4TmuSsYS56BbEIsbp/9lwN9e5WeAG33Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:24:22.280038Z"},"content_sha256":"56f01269d6c98da3180c1202e15160f68ffbf8bd44a7ebe1898e3728a0b959a5","schema_version":"1.0","event_id":"sha256:56f01269d6c98da3180c1202e15160f68ffbf8bd44a7ebe1898e3728a0b959a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FYSKFWMN656RX56AKV4VWJN5HN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The EM algorithm and the Laplace Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Niko Br\\\"ummer","submitted_at":"2014-01-24T07:50:28Z","abstract_excerpt":"The Laplace approximation calls for the computation of second derivatives at the likelihood maximum. When the maximum is found by the EM-algorithm, there is a convenient way to compute these derivatives. The likelihood gradient can be obtained from the EM-auxiliary, while the Hessian can be obtained from this gradient with the Pearlmutter trick."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6276","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":"2026-05-18T03:01:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fFOWDS/2t/qEuWbkdqZGnCGr72b0Wcg2ev/o+z7DFPjoqMbkBpc/yt+6SGnKxl4EaFcjyvWRGrTG8539KV58AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:24:22.280384Z"},"content_sha256":"d3159cf5665627b3555f7569c3766ff2840d17fdf77989fc1c367e8d5ce6a865","schema_version":"1.0","event_id":"sha256:d3159cf5665627b3555f7569c3766ff2840d17fdf77989fc1c367e8d5ce6a865"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FYSKFWMN656RX56AKV4VWJN5HN/bundle.json","state_url":"https://pith.science/pith/FYSKFWMN656RX56AKV4VWJN5HN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FYSKFWMN656RX56AKV4VWJN5HN/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":"2026-06-03T05:24:22Z","links":{"resolver":"https://pith.science/pith/FYSKFWMN656RX56AKV4VWJN5HN","bundle":"https://pith.science/pith/FYSKFWMN656RX56AKV4VWJN5HN/bundle.json","state":"https://pith.science/pith/FYSKFWMN656RX56AKV4VWJN5HN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FYSKFWMN656RX56AKV4VWJN5HN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FYSKFWMN656RX56AKV4VWJN5HN","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":"04afd8ed1d2747f74162d14904f962e08929dd8958ef839dd94fc97dc1174631","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-01-24T07:50:28Z","title_canon_sha256":"8a7bf41ce5a9bd212b7eb1f4cb8e94ff0ccd0a1cbe0a66a2fbf606d899f5af53"},"schema_version":"1.0","source":{"id":"1401.6276","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6276","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6276v1","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6276","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"pith_short_12","alias_value":"FYSKFWMN656R","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FYSKFWMN656RX56A","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FYSKFWMN","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:d3159cf5665627b3555f7569c3766ff2840d17fdf77989fc1c367e8d5ce6a865","target":"graph","created_at":"2026-05-18T03:01:12Z","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 Laplace approximation calls for the computation of second derivatives at the likelihood maximum. When the maximum is found by the EM-algorithm, there is a convenient way to compute these derivatives. The likelihood gradient can be obtained from the EM-auxiliary, while the Hessian can be obtained from this gradient with the Pearlmutter trick.","authors_text":"Niko Br\\\"ummer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-01-24T07:50:28Z","title":"The EM algorithm and the Laplace Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6276","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":"sha256:56f01269d6c98da3180c1202e15160f68ffbf8bd44a7ebe1898e3728a0b959a5","target":"record","created_at":"2026-05-18T03:01:12Z","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":"04afd8ed1d2747f74162d14904f962e08929dd8958ef839dd94fc97dc1174631","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-01-24T07:50:28Z","title_canon_sha256":"8a7bf41ce5a9bd212b7eb1f4cb8e94ff0ccd0a1cbe0a66a2fbf606d899f5af53"},"schema_version":"1.0","source":{"id":"1401.6276","kind":"arxiv","version":1}},"canonical_sha256":"2e24a2d98df77d1bf7c055795b25bd3b4dcd3919d07db3ac0ad98e311c7cfd67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e24a2d98df77d1bf7c055795b25bd3b4dcd3919d07db3ac0ad98e311c7cfd67","first_computed_at":"2026-05-18T03:01:12.614194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:12.614194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LBJDu5L2TmaNzzmDshsWWzg9Qba8sjo8PjpkzBxuzN/GwXQqWBWk4gYiEXZf0WiEQob87TT68r6WscG7Jc6iCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:12.614942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6276","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56f01269d6c98da3180c1202e15160f68ffbf8bd44a7ebe1898e3728a0b959a5","sha256:d3159cf5665627b3555f7569c3766ff2840d17fdf77989fc1c367e8d5ce6a865"],"state_sha256":"02409a969388fdf2c9628ddab8d2ed98b5c1452162a95148a9ec10804cf9ebfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1WfqCjP0E9xu8k7drKUnBrx6X9n6qB58e/IJz/ZeQU+uzFT9BJupm6a+OSAdV7nvmEmsfYDv8NGQ9Bd/MlqNDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:24:22.282240Z","bundle_sha256":"26b9cf643a7247dbb7e42cf4ddda7f3d5caab846dfc12fd8ba73507f258a6ca7"}}