{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:U6CTHKE4AFQOXCIMKF2KFJRF7C","short_pith_number":"pith:U6CTHKE4","schema_version":"1.0","canonical_sha256":"a78533a89c0160eb890c5174a2a625f8938bedbd6b52e251610b9e93b50f47ac","source":{"kind":"arxiv","id":"1603.08584","version":1},"attestation_state":"computed","paper":{"title":"Exponential Concentration of a Density Functional Estimator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Barnab\\'as P \\'oczos, Shashank Singh","submitted_at":"2016-03-28T23:01:31Z","abstract_excerpt":"We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For densities on the $d$-dimensional unit cube $[0,1]^d$ that lie in a $\\beta$-H\\\"older smoothness class, we prove our estimator converges at the rate $O \\left( n^{-\\frac{\\beta}{\\beta + d}} \\right)$. Furthermore, we prove the estimator is exponentially concentrated about its mean, whereas most previous related results have proven only expected error bounds on e"},"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":"1603.08584","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-28T23:01:31Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML","stat.TH"],"title_canon_sha256":"66358288852f0082b503983b66fec58cf3d2ac8de7946a7823b9cb5aa5b558a8","abstract_canon_sha256":"3bb2b2c6348742b0c7192e7440d88c21172399541d474a8e8a4ebec9a56be4aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:05.988762Z","signature_b64":"0M/Pf9sKjrCxEP9F94i7FUX9ELXzYnfO4tXuiiZQgMmDuC8EVzs/Yrf5gX1iaUJ4TQ7ssq0EDLjtScgoNJIJBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a78533a89c0160eb890c5174a2a625f8938bedbd6b52e251610b9e93b50f47ac","last_reissued_at":"2026-05-18T01:18:05.988049Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:05.988049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential Concentration of a Density Functional Estimator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Barnab\\'as P \\'oczos, Shashank Singh","submitted_at":"2016-03-28T23:01:31Z","abstract_excerpt":"We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For densities on the $d$-dimensional unit cube $[0,1]^d$ that lie in a $\\beta$-H\\\"older smoothness class, we prove our estimator converges at the rate $O \\left( n^{-\\frac{\\beta}{\\beta + d}} \\right)$. Furthermore, we prove the estimator is exponentially concentrated about its mean, whereas most previous related results have proven only expected error bounds on e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08584","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.08584","created_at":"2026-05-18T01:18:05.988154+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.08584v1","created_at":"2026-05-18T01:18:05.988154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08584","created_at":"2026-05-18T01:18:05.988154+00:00"},{"alias_kind":"pith_short_12","alias_value":"U6CTHKE4AFQO","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"U6CTHKE4AFQOXCIM","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"U6CTHKE4","created_at":"2026-05-18T12:30:46.583412+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/U6CTHKE4AFQOXCIMKF2KFJRF7C","json":"https://pith.science/pith/U6CTHKE4AFQOXCIMKF2KFJRF7C.json","graph_json":"https://pith.science/api/pith-number/U6CTHKE4AFQOXCIMKF2KFJRF7C/graph.json","events_json":"https://pith.science/api/pith-number/U6CTHKE4AFQOXCIMKF2KFJRF7C/events.json","paper":"https://pith.science/paper/U6CTHKE4"},"agent_actions":{"view_html":"https://pith.science/pith/U6CTHKE4AFQOXCIMKF2KFJRF7C","download_json":"https://pith.science/pith/U6CTHKE4AFQOXCIMKF2KFJRF7C.json","view_paper":"https://pith.science/paper/U6CTHKE4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.08584&json=true","fetch_graph":"https://pith.science/api/pith-number/U6CTHKE4AFQOXCIMKF2KFJRF7C/graph.json","fetch_events":"https://pith.science/api/pith-number/U6CTHKE4AFQOXCIMKF2KFJRF7C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U6CTHKE4AFQOXCIMKF2KFJRF7C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U6CTHKE4AFQOXCIMKF2KFJRF7C/action/storage_attestation","attest_author":"https://pith.science/pith/U6CTHKE4AFQOXCIMKF2KFJRF7C/action/author_attestation","sign_citation":"https://pith.science/pith/U6CTHKE4AFQOXCIMKF2KFJRF7C/action/citation_signature","submit_replication":"https://pith.science/pith/U6CTHKE4AFQOXCIMKF2KFJRF7C/action/replication_record"}},"created_at":"2026-05-18T01:18:05.988154+00:00","updated_at":"2026-05-18T01:18:05.988154+00:00"}