{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:33N7R6CW4JLYRU6NE5VZQDA75U","short_pith_number":"pith:33N7R6CW","canonical_record":{"source":{"id":"1210.2613","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-09T14:30:51Z","cross_cats_sorted":["cs.LG","math.IT","math.PR"],"title_canon_sha256":"b3c21a9eb2c6a993a9011727820d3663c9a29493ee8a1beaea180b5fc64b9e37","abstract_canon_sha256":"c0ec77cfc5ccba81456089fe07a2c3bacfa2551b4c60b3a1d14000e973b712e5"},"schema_version":"1.0"},"canonical_sha256":"dedbf8f856e25788d3cd276b980c1fed1ecf7352d9bb0d70f27f487113edf2da","source":{"kind":"arxiv","id":"1210.2613","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2613","created_at":"2026-05-18T01:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2613v2","created_at":"2026-05-18T01:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2613","created_at":"2026-05-18T01:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"33N7R6CW4JLY","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"33N7R6CW4JLYRU6N","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"33N7R6CW","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:33N7R6CW4JLYRU6NE5VZQDA75U","target":"record","payload":{"canonical_record":{"source":{"id":"1210.2613","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-09T14:30:51Z","cross_cats_sorted":["cs.LG","math.IT","math.PR"],"title_canon_sha256":"b3c21a9eb2c6a993a9011727820d3663c9a29493ee8a1beaea180b5fc64b9e37","abstract_canon_sha256":"c0ec77cfc5ccba81456089fe07a2c3bacfa2551b4c60b3a1d14000e973b712e5"},"schema_version":"1.0"},"canonical_sha256":"dedbf8f856e25788d3cd276b980c1fed1ecf7352d9bb0d70f27f487113edf2da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:04.070921Z","signature_b64":"NdZVx/HjfDLtKGHIc8RVs1iSTBMuHzRy7MsgewUemRu90tMjtbsHfOuUkmvf72k6VK0VMZ6fqvGleUyi+98yBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dedbf8f856e25788d3cd276b980c1fed1ecf7352d9bb0d70f27f487113edf2da","last_reissued_at":"2026-05-18T01:54:04.070349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:04.070349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.2613","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":"2026-05-18T01:54:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sVHa0avxAQGOrRI/5g1N1iBOT0WT6SIFHtRA1+NJg2BrdhFtI8pwt9Nb1y4G2ckejWizoSIXvNAFo1HbZMCsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:04:09.295438Z"},"content_sha256":"2aa4bae0a4cc14c81f6b15d7579596268fd30d5926a74b689d1387fd848bf2f9","schema_version":"1.0","event_id":"sha256:2aa4bae0a4cc14c81f6b15d7579596268fd30d5926a74b689d1387fd848bf2f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:33N7R6CW4JLYRU6NE5VZQDA75U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measuring the Influence of Observations in HMMs through the Kullback-Leibler Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Gregory Nuel, Vittorio Perduca","submitted_at":"2012-10-09T14:30:51Z","abstract_excerpt":"We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the conditional distribution of the hidden states' chain given the complete sequence of observations and the conditional distribution of the hidden chain given all the observations but the one under consideration. We introduce a linear complexity algorithm for computing the influence of all the observations. As an illustration, we investigate the application of our algorithm to the problem "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2613","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":"2026-05-18T01:54:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/keSMx9eM7RZGIyTYlbajrLcbRH4E7Fp4RyfF+lZgfzvhMLN0RC+TQIOafYS+w/BkmGANUAd0qbKZZnVKihyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:04:09.296304Z"},"content_sha256":"74b1c418d235af8a12555d88ea29502bbbd6fa74cb9138ff4eb9937f35c4a2fa","schema_version":"1.0","event_id":"sha256:74b1c418d235af8a12555d88ea29502bbbd6fa74cb9138ff4eb9937f35c4a2fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/33N7R6CW4JLYRU6NE5VZQDA75U/bundle.json","state_url":"https://pith.science/pith/33N7R6CW4JLYRU6NE5VZQDA75U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/33N7R6CW4JLYRU6NE5VZQDA75U/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":"2026-05-31T19:04:09Z","links":{"resolver":"https://pith.science/pith/33N7R6CW4JLYRU6NE5VZQDA75U","bundle":"https://pith.science/pith/33N7R6CW4JLYRU6NE5VZQDA75U/bundle.json","state":"https://pith.science/pith/33N7R6CW4JLYRU6NE5VZQDA75U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/33N7R6CW4JLYRU6NE5VZQDA75U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:33N7R6CW4JLYRU6NE5VZQDA75U","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":"c0ec77cfc5ccba81456089fe07a2c3bacfa2551b4c60b3a1d14000e973b712e5","cross_cats_sorted":["cs.LG","math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-09T14:30:51Z","title_canon_sha256":"b3c21a9eb2c6a993a9011727820d3663c9a29493ee8a1beaea180b5fc64b9e37"},"schema_version":"1.0","source":{"id":"1210.2613","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2613","created_at":"2026-05-18T01:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2613v2","created_at":"2026-05-18T01:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2613","created_at":"2026-05-18T01:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"33N7R6CW4JLY","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"33N7R6CW4JLYRU6N","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"33N7R6CW","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:74b1c418d235af8a12555d88ea29502bbbd6fa74cb9138ff4eb9937f35c4a2fa","target":"graph","created_at":"2026-05-18T01:54:04Z","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":"We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the conditional distribution of the hidden states' chain given the complete sequence of observations and the conditional distribution of the hidden chain given all the observations but the one under consideration. We introduce a linear complexity algorithm for computing the influence of all the observations. As an illustration, we investigate the application of our algorithm to the problem ","authors_text":"Gregory Nuel, Vittorio Perduca","cross_cats":["cs.LG","math.IT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-09T14:30:51Z","title":"Measuring the Influence of Observations in HMMs through the Kullback-Leibler Distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2613","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":"sha256:2aa4bae0a4cc14c81f6b15d7579596268fd30d5926a74b689d1387fd848bf2f9","target":"record","created_at":"2026-05-18T01:54:04Z","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":"c0ec77cfc5ccba81456089fe07a2c3bacfa2551b4c60b3a1d14000e973b712e5","cross_cats_sorted":["cs.LG","math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-10-09T14:30:51Z","title_canon_sha256":"b3c21a9eb2c6a993a9011727820d3663c9a29493ee8a1beaea180b5fc64b9e37"},"schema_version":"1.0","source":{"id":"1210.2613","kind":"arxiv","version":2}},"canonical_sha256":"dedbf8f856e25788d3cd276b980c1fed1ecf7352d9bb0d70f27f487113edf2da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dedbf8f856e25788d3cd276b980c1fed1ecf7352d9bb0d70f27f487113edf2da","first_computed_at":"2026-05-18T01:54:04.070349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:54:04.070349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NdZVx/HjfDLtKGHIc8RVs1iSTBMuHzRy7MsgewUemRu90tMjtbsHfOuUkmvf72k6VK0VMZ6fqvGleUyi+98yBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:54:04.070921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2613","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2aa4bae0a4cc14c81f6b15d7579596268fd30d5926a74b689d1387fd848bf2f9","sha256:74b1c418d235af8a12555d88ea29502bbbd6fa74cb9138ff4eb9937f35c4a2fa"],"state_sha256":"f274af9bd0ca75541f4022b73a22a22b77caaa33773f5df855a5a6c6e77b9eef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mI2x1qArFzbXsGPdSqdrwj/Z3m0xj4cr+MlVmg3masE0BSOtMJlx9JScD1znWRec6dK5MdtVDQ9ERPwwTHNrDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:04:09.301051Z","bundle_sha256":"99b7b727e62e3dc0cb48565705a6f8b0cebeff7b97c8d8f6183b90f33f8073ab"}}