{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BF4FCE2DNDMY2Q3TW4ZZ77MIUS","short_pith_number":"pith:BF4FCE2D","canonical_record":{"source":{"id":"1810.03730","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-08T22:21:49Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3548f210b0e7063605473a4d63e643212e98ac8a8ca786e6436e8caf5c7c2775","abstract_canon_sha256":"c648faf90c2985785b01f6f63809401e6651e4a74e4a9267004918fe114af820"},"schema_version":"1.0"},"canonical_sha256":"097851134368d98d4373b7339ffd88a4b6ae74aa28d0ad676909826e25d2453e","source":{"kind":"arxiv","id":"1810.03730","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03730","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03730v5","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03730","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"BF4FCE2DNDMY","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"pith_short_16","alias_value":"BF4FCE2DNDMY2Q3T","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"pith_short_8","alias_value":"BF4FCE2D","created_at":"2026-07-05T04:14:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BF4FCE2DNDMY2Q3TW4ZZ77MIUS","target":"record","payload":{"canonical_record":{"source":{"id":"1810.03730","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-08T22:21:49Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3548f210b0e7063605473a4d63e643212e98ac8a8ca786e6436e8caf5c7c2775","abstract_canon_sha256":"c648faf90c2985785b01f6f63809401e6651e4a74e4a9267004918fe114af820"},"schema_version":"1.0"},"canonical_sha256":"097851134368d98d4373b7339ffd88a4b6ae74aa28d0ad676909826e25d2453e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:14:21.687276Z","signature_b64":"i30qBxXOtedN7aZf29+WEWwibXja66GKe+V/wI6fKvBZdgiurZI94gNnPUP/MWJf+agPcmyEUvHnoCsQhz/FCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"097851134368d98d4373b7339ffd88a4b6ae74aa28d0ad676909826e25d2453e","last_reissued_at":"2026-07-05T04:14:21.686875Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:14:21.686875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.03730","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:14:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IKy/AnkksUxKK0LQMhMEsYasluUl4JL0dGHN1V6pbmakbVcGdGVFYV6hYneKn3wgoip09fkPSIVcasP0mOVgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T21:12:11.951761Z"},"content_sha256":"5611f0649f45a1d75d50bb6cba4a1e47e76c2624b30a3cc837e15934f69a087c","schema_version":"1.0","event_id":"sha256:5611f0649f45a1d75d50bb6cba4a1e47e76c2624b30a3cc837e15934f69a087c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BF4FCE2DNDMY2Q3TW4ZZ77MIUS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Non-parametric Bayesian Hawkes Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Christian Walder, Lexing Xie, Marian-Andrei Rizoiu, Rui Zhang","submitted_at":"2018-10-08T22:21:49Z","abstract_excerpt":"In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their uncertainty. Our method is based on the cluster representation of Hawkes processes. Utilizing the finite support assumption of the Hawkes process, we efficiently sample random branching structures and thus, we split the Hawkes process into clusters of Poisson processes. We derive two algorithms -- a block Gibbs sampler and a maximum a posteriori estimator based on e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03730","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.03730/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:14:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ZfF0hOIMZvWPrEdEesnigrisEaWCR7MrBs1jDwrRuebldE1DALXikZ4/kuM6pvShH0O9ALofhq3Fceo3LdBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T21:12:11.952152Z"},"content_sha256":"483883d1b792ea675fa8a79c8a9bbd2a025094a4611338a26bc5afb80ede5944","schema_version":"1.0","event_id":"sha256:483883d1b792ea675fa8a79c8a9bbd2a025094a4611338a26bc5afb80ede5944"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BF4FCE2DNDMY2Q3TW4ZZ77MIUS/bundle.json","state_url":"https://pith.science/pith/BF4FCE2DNDMY2Q3TW4ZZ77MIUS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BF4FCE2DNDMY2Q3TW4ZZ77MIUS/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":"2026-08-05T21:12:11Z","links":{"resolver":"https://pith.science/pith/BF4FCE2DNDMY2Q3TW4ZZ77MIUS","bundle":"https://pith.science/pith/BF4FCE2DNDMY2Q3TW4ZZ77MIUS/bundle.json","state":"https://pith.science/pith/BF4FCE2DNDMY2Q3TW4ZZ77MIUS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BF4FCE2DNDMY2Q3TW4ZZ77MIUS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BF4FCE2DNDMY2Q3TW4ZZ77MIUS","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":"c648faf90c2985785b01f6f63809401e6651e4a74e4a9267004918fe114af820","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-08T22:21:49Z","title_canon_sha256":"3548f210b0e7063605473a4d63e643212e98ac8a8ca786e6436e8caf5c7c2775"},"schema_version":"1.0","source":{"id":"1810.03730","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03730","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03730v5","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03730","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"BF4FCE2DNDMY","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"pith_short_16","alias_value":"BF4FCE2DNDMY2Q3T","created_at":"2026-07-05T04:14:21Z"},{"alias_kind":"pith_short_8","alias_value":"BF4FCE2D","created_at":"2026-07-05T04:14:21Z"}],"graph_snapshots":[{"event_id":"sha256:483883d1b792ea675fa8a79c8a9bbd2a025094a4611338a26bc5afb80ede5944","target":"graph","created_at":"2026-07-05T04:14:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1810.03730/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their uncertainty. Our method is based on the cluster representation of Hawkes processes. Utilizing the finite support assumption of the Hawkes process, we efficiently sample random branching structures and thus, we split the Hawkes process into clusters of Poisson processes. We derive two algorithms -- a block Gibbs sampler and a maximum a posteriori estimator based on e","authors_text":"Christian Walder, Lexing Xie, Marian-Andrei Rizoiu, Rui Zhang","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-08T22:21:49Z","title":"Efficient Non-parametric Bayesian Hawkes Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03730","kind":"arxiv","version":5},"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":"sha256:5611f0649f45a1d75d50bb6cba4a1e47e76c2624b30a3cc837e15934f69a087c","target":"record","created_at":"2026-07-05T04:14:21Z","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":"c648faf90c2985785b01f6f63809401e6651e4a74e4a9267004918fe114af820","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-10-08T22:21:49Z","title_canon_sha256":"3548f210b0e7063605473a4d63e643212e98ac8a8ca786e6436e8caf5c7c2775"},"schema_version":"1.0","source":{"id":"1810.03730","kind":"arxiv","version":5}},"canonical_sha256":"097851134368d98d4373b7339ffd88a4b6ae74aa28d0ad676909826e25d2453e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"097851134368d98d4373b7339ffd88a4b6ae74aa28d0ad676909826e25d2453e","first_computed_at":"2026-07-05T04:14:21.686875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:14:21.686875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i30qBxXOtedN7aZf29+WEWwibXja66GKe+V/wI6fKvBZdgiurZI94gNnPUP/MWJf+agPcmyEUvHnoCsQhz/FCA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:14:21.687276Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03730","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5611f0649f45a1d75d50bb6cba4a1e47e76c2624b30a3cc837e15934f69a087c","sha256:483883d1b792ea675fa8a79c8a9bbd2a025094a4611338a26bc5afb80ede5944"],"state_sha256":"215e4e10e02a82faa1d25b086e631a4b76d9696d54a7b65d320be31ca471c83b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ycSCnvjcTbYLsnQrSCPgbUeNG3ypvRdldjKccRsJuLdMkxGeazUrsntsi9IVr7XPtbJ/7VWzh2B1SDC21OSBCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T21:12:11.954801Z","bundle_sha256":"c5b90e059de972360433b8e7fbe89aead141c9aa6096ba441bea9df20a1d058a"}}