{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NGCDN7I5J5HKSYU4XOY256IJ3L","short_pith_number":"pith:NGCDN7I5","schema_version":"1.0","canonical_sha256":"698436fd1d4f4ea9629cbbb1aef909dac958b5aea76023d676cb905e89ebe237","source":{"kind":"arxiv","id":"1702.01591","version":2},"attestation_state":"computed","paper":{"title":"The Partial Entropy Decomposition: Decomposing multivariate entropy and mutual information via pointwise common surprisal","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.IT","math.ST","q-bio.NC","q-bio.QM","stat.ME","stat.TH"],"primary_cat":"cs.IT","authors_text":"Robin A. A. Ince","submitted_at":"2017-02-06T12:28:27Z","abstract_excerpt":"Obtaining meaningful quantitative descriptions of the statistical dependence within multivariate systems is a difficult open problem. Recently, the Partial Information Decomposition (PID) was proposed to decompose mutual information (MI) about a target variable into components which are redundant, unique and synergistic within different subsets of predictor variables. Here, we propose to apply the elegant formalism of the PID to multivariate entropy, resulting in a Partial Entropy Decomposition (PED). We implement the PED with an entropy redundancy measure based on pointwise common surprisal; "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.01591","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.IT","submitted_at":"2017-02-06T12:28:27Z","cross_cats_sorted":["math.IT","math.ST","q-bio.NC","q-bio.QM","stat.ME","stat.TH"],"title_canon_sha256":"0b40219c52ea4c59aa7a331aa0ea1356227d19c9913bdadd0ab86cde8e907b91","abstract_canon_sha256":"7f9eef009fb73c73647b09f067f309096dd43fb0d5a1e8c196322022687a3e8e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:28.573471Z","signature_b64":"YYfuVHnHS4Rzd3hKx897lrysNUu8cSEEeOTQAfJJxckHxIEd4cDpJ6y8SqREU1HUumV+KapiBy/4t6KCmEJwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"698436fd1d4f4ea9629cbbb1aef909dac958b5aea76023d676cb905e89ebe237","last_reissued_at":"2026-05-18T00:50:28.572745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:28.572745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Partial Entropy Decomposition: Decomposing multivariate entropy and mutual information via pointwise common surprisal","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.IT","math.ST","q-bio.NC","q-bio.QM","stat.ME","stat.TH"],"primary_cat":"cs.IT","authors_text":"Robin A. A. Ince","submitted_at":"2017-02-06T12:28:27Z","abstract_excerpt":"Obtaining meaningful quantitative descriptions of the statistical dependence within multivariate systems is a difficult open problem. Recently, the Partial Information Decomposition (PID) was proposed to decompose mutual information (MI) about a target variable into components which are redundant, unique and synergistic within different subsets of predictor variables. Here, we propose to apply the elegant formalism of the PID to multivariate entropy, resulting in a Partial Entropy Decomposition (PED). We implement the PED with an entropy redundancy measure based on pointwise common surprisal; "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01591","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1702.01591","created_at":"2026-05-18T00:50:28.572860+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.01591v2","created_at":"2026-05-18T00:50:28.572860+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01591","created_at":"2026-05-18T00:50:28.572860+00:00"},{"alias_kind":"pith_short_12","alias_value":"NGCDN7I5J5HK","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"NGCDN7I5J5HKSYU4","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"NGCDN7I5","created_at":"2026-05-18T12:31:31.346846+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2402.03554","citing_title":"Explicit Formula for Partial Information Decomposition","ref_index":4,"is_internal_anchor":true},{"citing_arxiv_id":"2506.18498","citing_title":"A scalable estimator of higher-order information in complex dynamical systems","ref_index":78,"is_internal_anchor":true},{"citing_arxiv_id":"2508.05530","citing_title":"Multivariate Partial Information Decomposition: Constructions, Inconsistencies, and Alternative Measures","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2604.03869","citing_title":"Structural Impossibility of Antichain-Lattice Partial Information Decomposition","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NGCDN7I5J5HKSYU4XOY256IJ3L","json":"https://pith.science/pith/NGCDN7I5J5HKSYU4XOY256IJ3L.json","graph_json":"https://pith.science/api/pith-number/NGCDN7I5J5HKSYU4XOY256IJ3L/graph.json","events_json":"https://pith.science/api/pith-number/NGCDN7I5J5HKSYU4XOY256IJ3L/events.json","paper":"https://pith.science/paper/NGCDN7I5"},"agent_actions":{"view_html":"https://pith.science/pith/NGCDN7I5J5HKSYU4XOY256IJ3L","download_json":"https://pith.science/pith/NGCDN7I5J5HKSYU4XOY256IJ3L.json","view_paper":"https://pith.science/paper/NGCDN7I5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.01591&json=true","fetch_graph":"https://pith.science/api/pith-number/NGCDN7I5J5HKSYU4XOY256IJ3L/graph.json","fetch_events":"https://pith.science/api/pith-number/NGCDN7I5J5HKSYU4XOY256IJ3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NGCDN7I5J5HKSYU4XOY256IJ3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NGCDN7I5J5HKSYU4XOY256IJ3L/action/storage_attestation","attest_author":"https://pith.science/pith/NGCDN7I5J5HKSYU4XOY256IJ3L/action/author_attestation","sign_citation":"https://pith.science/pith/NGCDN7I5J5HKSYU4XOY256IJ3L/action/citation_signature","submit_replication":"https://pith.science/pith/NGCDN7I5J5HKSYU4XOY256IJ3L/action/replication_record"}},"created_at":"2026-05-18T00:50:28.572860+00:00","updated_at":"2026-05-18T00:50:28.572860+00:00"}