{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:MEI3IYAPIGEDJ5VWXQ5PEVASOE","short_pith_number":"pith:MEI3IYAP","schema_version":"1.0","canonical_sha256":"6111b4600f418834f6b6bc3af254127138f3c73bf7dd4e1038c68b319ce38823","source":{"kind":"arxiv","id":"2402.07747","version":2},"attestation_state":"computed","paper":{"title":"Optimal score estimation via empirical Bayes smoothing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Andre Wibisono, Kaylee Yingxi Yang, Yihong Wu","submitted_at":"2024-02-12T16:17:40Z","abstract_excerpt":"We study the problem of estimating the score function of an unknown probability distribution $\\rho^*$ from $n$ independent and identically distributed observations in $d$ dimensions. Assuming that $\\rho^*$ is subgaussian and has a Lipschitz-continuous score function $s^*$, we establish the optimal rate of $\\tilde \\Theta(n^{-\\frac{2}{d+4}})$ for this estimation problem under the loss function $\\|\\hat s - s^*\\|^2_{L^2(\\rho^*)}$ that is commonly used in the score matching literature, highlighting the curse of dimensionality where sample complexity for accurate score estimation grows exponentially"},"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":"2402.07747","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-02-12T16:17:40Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"922f6c96a20124e3a8983698f1a315af594fc0217ced90fd69b4a201e31ae7e7","abstract_canon_sha256":"8ad6275d9a9400d4036bda9dcfd773ac8e1b0ebdb5905008216b4f3f05da2161"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:30:50.229827Z","signature_b64":"3Ota6TjcUV/4mucIMzJdsaQQkwoiD3pc76h3rFR/7SO7a9zJTKDMJld6CBbs7Fv5454icd9otJGoM3fpt0XlAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6111b4600f418834f6b6bc3af254127138f3c73bf7dd4e1038c68b319ce38823","last_reissued_at":"2026-07-05T08:30:50.229354Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:30:50.229354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal score estimation via empirical Bayes smoothing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Andre Wibisono, Kaylee Yingxi Yang, Yihong Wu","submitted_at":"2024-02-12T16:17:40Z","abstract_excerpt":"We study the problem of estimating the score function of an unknown probability distribution $\\rho^*$ from $n$ independent and identically distributed observations in $d$ dimensions. Assuming that $\\rho^*$ is subgaussian and has a Lipschitz-continuous score function $s^*$, we establish the optimal rate of $\\tilde \\Theta(n^{-\\frac{2}{d+4}})$ for this estimation problem under the loss function $\\|\\hat s - s^*\\|^2_{L^2(\\rho^*)}$ that is commonly used in the score matching literature, highlighting the curse of dimensionality where sample complexity for accurate score estimation grows exponentially"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07747","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.07747/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2402.07747","created_at":"2026-07-05T08:30:50.229416+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.07747v2","created_at":"2026-07-05T08:30:50.229416+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.07747","created_at":"2026-07-05T08:30:50.229416+00:00"},{"alias_kind":"pith_short_12","alias_value":"MEI3IYAPIGED","created_at":"2026-07-05T08:30:50.229416+00:00"},{"alias_kind":"pith_short_16","alias_value":"MEI3IYAPIGEDJ5VW","created_at":"2026-07-05T08:30:50.229416+00:00"},{"alias_kind":"pith_short_8","alias_value":"MEI3IYAP","created_at":"2026-07-05T08:30:50.229416+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.23627","citing_title":"Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choices","ref_index":51,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MEI3IYAPIGEDJ5VWXQ5PEVASOE","json":"https://pith.science/pith/MEI3IYAPIGEDJ5VWXQ5PEVASOE.json","graph_json":"https://pith.science/api/pith-number/MEI3IYAPIGEDJ5VWXQ5PEVASOE/graph.json","events_json":"https://pith.science/api/pith-number/MEI3IYAPIGEDJ5VWXQ5PEVASOE/events.json","paper":"https://pith.science/paper/MEI3IYAP"},"agent_actions":{"view_html":"https://pith.science/pith/MEI3IYAPIGEDJ5VWXQ5PEVASOE","download_json":"https://pith.science/pith/MEI3IYAPIGEDJ5VWXQ5PEVASOE.json","view_paper":"https://pith.science/paper/MEI3IYAP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.07747&json=true","fetch_graph":"https://pith.science/api/pith-number/MEI3IYAPIGEDJ5VWXQ5PEVASOE/graph.json","fetch_events":"https://pith.science/api/pith-number/MEI3IYAPIGEDJ5VWXQ5PEVASOE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MEI3IYAPIGEDJ5VWXQ5PEVASOE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MEI3IYAPIGEDJ5VWXQ5PEVASOE/action/storage_attestation","attest_author":"https://pith.science/pith/MEI3IYAPIGEDJ5VWXQ5PEVASOE/action/author_attestation","sign_citation":"https://pith.science/pith/MEI3IYAPIGEDJ5VWXQ5PEVASOE/action/citation_signature","submit_replication":"https://pith.science/pith/MEI3IYAPIGEDJ5VWXQ5PEVASOE/action/replication_record"}},"created_at":"2026-07-05T08:30:50.229416+00:00","updated_at":"2026-07-05T08:30:50.229416+00:00"}