{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:J6CNE73NZL4FJ3CGQHXZ247QO2","short_pith_number":"pith:J6CNE73N","schema_version":"1.0","canonical_sha256":"4f84d27f6dcaf854ec4681ef9d73f0769c771c3d1ec8e28656957f0af99552e2","source":{"kind":"arxiv","id":"1201.2334","version":4},"attestation_state":"computed","paper":{"title":"Universal Estimation of Directed Information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Haim H. Permuter, Jiantao Jiao, Lei Zhao, Tsachy Weissman, Young-Han Kim","submitted_at":"2012-01-11T15:49:51Z","abstract_excerpt":"Four estimators of the directed information rate between a pair of jointly stationary ergodic finite-alphabet processes are proposed, based on universal probability assignments. The first one is a Shannon--McMillan--Breiman type estimator, similar to those used by Verd\\'u (2005) and Cai, Kulkarni, and Verd\\'u (2006) for estimation of other information measures. We show the almost sure and $L_1$ convergence properties of the estimator for any underlying universal probability assignment. The other three estimators map universal probability assignments to different functionals, each exhibiting re"},"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":"1201.2334","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-01-11T15:49:51Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"2a2ae4727c75951b6a1258abedacb5fb10d62176f377779fa2e349f68c9be69c","abstract_canon_sha256":"2ab2b04bd9996a44445d1145923ce5657cee219540887a928cea30c86723fc42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:09.961870Z","signature_b64":"gSFR/WvrqJpxRUb9d4AM5TXiHdkRJVwRm9G/DLNZaXDMAjkT7N122gvUx1yD2akS4XPEYoAJ6Oud5iVKZI8bDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f84d27f6dcaf854ec4681ef9d73f0769c771c3d1ec8e28656957f0af99552e2","last_reissued_at":"2026-05-18T00:59:09.961144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:09.961144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal Estimation of Directed Information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Haim H. Permuter, Jiantao Jiao, Lei Zhao, Tsachy Weissman, Young-Han Kim","submitted_at":"2012-01-11T15:49:51Z","abstract_excerpt":"Four estimators of the directed information rate between a pair of jointly stationary ergodic finite-alphabet processes are proposed, based on universal probability assignments. The first one is a Shannon--McMillan--Breiman type estimator, similar to those used by Verd\\'u (2005) and Cai, Kulkarni, and Verd\\'u (2006) for estimation of other information measures. We show the almost sure and $L_1$ convergence properties of the estimator for any underlying universal probability assignment. The other three estimators map universal probability assignments to different functionals, each exhibiting re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2334","kind":"arxiv","version":4},"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":"1201.2334","created_at":"2026-05-18T00:59:09.961254+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.2334v4","created_at":"2026-05-18T00:59:09.961254+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2334","created_at":"2026-05-18T00:59:09.961254+00:00"},{"alias_kind":"pith_short_12","alias_value":"J6CNE73NZL4F","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"J6CNE73NZL4FJ3CG","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"J6CNE73N","created_at":"2026-05-18T12:27:11.947152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J6CNE73NZL4FJ3CGQHXZ247QO2","json":"https://pith.science/pith/J6CNE73NZL4FJ3CGQHXZ247QO2.json","graph_json":"https://pith.science/api/pith-number/J6CNE73NZL4FJ3CGQHXZ247QO2/graph.json","events_json":"https://pith.science/api/pith-number/J6CNE73NZL4FJ3CGQHXZ247QO2/events.json","paper":"https://pith.science/paper/J6CNE73N"},"agent_actions":{"view_html":"https://pith.science/pith/J6CNE73NZL4FJ3CGQHXZ247QO2","download_json":"https://pith.science/pith/J6CNE73NZL4FJ3CGQHXZ247QO2.json","view_paper":"https://pith.science/paper/J6CNE73N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.2334&json=true","fetch_graph":"https://pith.science/api/pith-number/J6CNE73NZL4FJ3CGQHXZ247QO2/graph.json","fetch_events":"https://pith.science/api/pith-number/J6CNE73NZL4FJ3CGQHXZ247QO2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J6CNE73NZL4FJ3CGQHXZ247QO2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J6CNE73NZL4FJ3CGQHXZ247QO2/action/storage_attestation","attest_author":"https://pith.science/pith/J6CNE73NZL4FJ3CGQHXZ247QO2/action/author_attestation","sign_citation":"https://pith.science/pith/J6CNE73NZL4FJ3CGQHXZ247QO2/action/citation_signature","submit_replication":"https://pith.science/pith/J6CNE73NZL4FJ3CGQHXZ247QO2/action/replication_record"}},"created_at":"2026-05-18T00:59:09.961254+00:00","updated_at":"2026-05-18T00:59:09.961254+00:00"}