{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:747ZUAA2AUHAWA2VNDVXZRU2AU","short_pith_number":"pith:747ZUAA2","schema_version":"1.0","canonical_sha256":"ff3f9a001a050e0b035568eb7cc69a0535ee301e87f6b0b47ca8437683d96461","source":{"kind":"arxiv","id":"1112.1450","version":2},"attestation_state":"computed","paper":{"title":"A recursive procedure for density estimation on the binary hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Jorge Silva, Maxim Raginsky, Rebecca Willett, Svetlana Lazebnik","submitted_at":"2011-12-07T00:30:17Z","abstract_excerpt":"This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients to estimate, which renders conventional approaches computationally prohibitive when $d$ is large. However, for a wide class of densities that satisfy a certain sparsity condition, our estimator runs in probabilistic polynomial time and adapts to the unknown sparsity of the underlying density in two key ways: (1) it attains near-minimax mean-squared error fo"},"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":"1112.1450","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-12-07T00:30:17Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"d6051068986af030eb7c05abc3cd970794599f79dac735df138b4dd8a35db969","abstract_canon_sha256":"125cf2687f5e38461462002329bb613ff0651d1d819d64cd89e2292118fc6a3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:41.864393Z","signature_b64":"bBOxvq50mneZR3n7mR83hAq0Qn/0uPe7wFMFGrFdMU98SiMMIdsMbSLIzzx4DBVZ3Pni38PtrVhr5ONV1Jj0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff3f9a001a050e0b035568eb7cc69a0535ee301e87f6b0b47ca8437683d96461","last_reissued_at":"2026-05-18T03:39:41.863585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:41.863585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A recursive procedure for density estimation on the binary hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Jorge Silva, Maxim Raginsky, Rebecca Willett, Svetlana Lazebnik","submitted_at":"2011-12-07T00:30:17Z","abstract_excerpt":"This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients to estimate, which renders conventional approaches computationally prohibitive when $d$ is large. However, for a wide class of densities that satisfy a certain sparsity condition, our estimator runs in probabilistic polynomial time and adapts to the unknown sparsity of the underlying density in two key ways: (1) it attains near-minimax mean-squared error fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1450","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":"1112.1450","created_at":"2026-05-18T03:39:41.863705+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.1450v2","created_at":"2026-05-18T03:39:41.863705+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1450","created_at":"2026-05-18T03:39:41.863705+00:00"},{"alias_kind":"pith_short_12","alias_value":"747ZUAA2AUHA","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"747ZUAA2AUHAWA2V","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"747ZUAA2","created_at":"2026-05-18T12:26:22.705136+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/747ZUAA2AUHAWA2VNDVXZRU2AU","json":"https://pith.science/pith/747ZUAA2AUHAWA2VNDVXZRU2AU.json","graph_json":"https://pith.science/api/pith-number/747ZUAA2AUHAWA2VNDVXZRU2AU/graph.json","events_json":"https://pith.science/api/pith-number/747ZUAA2AUHAWA2VNDVXZRU2AU/events.json","paper":"https://pith.science/paper/747ZUAA2"},"agent_actions":{"view_html":"https://pith.science/pith/747ZUAA2AUHAWA2VNDVXZRU2AU","download_json":"https://pith.science/pith/747ZUAA2AUHAWA2VNDVXZRU2AU.json","view_paper":"https://pith.science/paper/747ZUAA2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.1450&json=true","fetch_graph":"https://pith.science/api/pith-number/747ZUAA2AUHAWA2VNDVXZRU2AU/graph.json","fetch_events":"https://pith.science/api/pith-number/747ZUAA2AUHAWA2VNDVXZRU2AU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/747ZUAA2AUHAWA2VNDVXZRU2AU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/747ZUAA2AUHAWA2VNDVXZRU2AU/action/storage_attestation","attest_author":"https://pith.science/pith/747ZUAA2AUHAWA2VNDVXZRU2AU/action/author_attestation","sign_citation":"https://pith.science/pith/747ZUAA2AUHAWA2VNDVXZRU2AU/action/citation_signature","submit_replication":"https://pith.science/pith/747ZUAA2AUHAWA2VNDVXZRU2AU/action/replication_record"}},"created_at":"2026-05-18T03:39:41.863705+00:00","updated_at":"2026-05-18T03:39:41.863705+00:00"}