{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QGJ5F7D2UUG4V344BGH72D2NHC","short_pith_number":"pith:QGJ5F7D2","schema_version":"1.0","canonical_sha256":"8193d2fc7aa50dcaef9c098ffd0f4d38aa41ba3aedf21873f88653885ee17aa6","source":{"kind":"arxiv","id":"1301.7390","version":1},"attestation_state":"computed","paper":{"title":"Hierarchical Mixtures-of-Experts for Exponential Family Regression Models with Generalized Linear Mean Functions: A Survey of Approximation and Consistency Results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Martin A. Tanner, Wenxin Jiang","submitted_at":"2013-01-30T15:04:59Z","abstract_excerpt":"We investigate a class of hierarchical mixtures-of-experts (HME) models where exponential family  regression models with generalized linear mean functions of the form psi(ga+fx^Tfgb) are mixed.  Here psi(...) is the inverse link function. Suppose the true response y follows an exponential  family regression model with mean function belonging to a class of smooth functions of the form psi(h(fx)) where h(...)in W_2^infty (a Sobolev class over [0,1]^{s}). It is shown that the HME probability density functions can approximate the true density, at a rate of O(m^{-2/s}) in L_p norm, and at a rate of"},"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":"1301.7390","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-01-30T15:04:59Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"51383b93cad7f01465154308f18e5973001fa68666d46eba9a7407c6bc3e388a","abstract_canon_sha256":"3e1a6a94fb78295acca74951acf70537bc954efeb88ac37f9355ec74fb214a84"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:00.075613Z","signature_b64":"nOgVPdI38NkGKQBT6j28aEu7gb8HVEgBCW6KkuXQ406sFxoMRkTDF7Ad+AJ3S7m8K1UdCQOJqLvOvsrJBXY+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8193d2fc7aa50dcaef9c098ffd0f4d38aa41ba3aedf21873f88653885ee17aa6","last_reissued_at":"2026-05-18T03:35:00.074894Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:00.074894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hierarchical Mixtures-of-Experts for Exponential Family Regression Models with Generalized Linear Mean Functions: A Survey of Approximation and Consistency Results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Martin A. Tanner, Wenxin Jiang","submitted_at":"2013-01-30T15:04:59Z","abstract_excerpt":"We investigate a class of hierarchical mixtures-of-experts (HME) models where exponential family  regression models with generalized linear mean functions of the form psi(ga+fx^Tfgb) are mixed.  Here psi(...) is the inverse link function. Suppose the true response y follows an exponential  family regression model with mean function belonging to a class of smooth functions of the form psi(h(fx)) where h(...)in W_2^infty (a Sobolev class over [0,1]^{s}). It is shown that the HME probability density functions can approximate the true density, at a rate of O(m^{-2/s}) in L_p norm, and at a rate of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7390","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":"1301.7390","created_at":"2026-05-18T03:35:00.074997+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.7390v1","created_at":"2026-05-18T03:35:00.074997+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7390","created_at":"2026-05-18T03:35:00.074997+00:00"},{"alias_kind":"pith_short_12","alias_value":"QGJ5F7D2UUG4","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QGJ5F7D2UUG4V344","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QGJ5F7D2","created_at":"2026-05-18T12:27:57.521954+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/QGJ5F7D2UUG4V344BGH72D2NHC","json":"https://pith.science/pith/QGJ5F7D2UUG4V344BGH72D2NHC.json","graph_json":"https://pith.science/api/pith-number/QGJ5F7D2UUG4V344BGH72D2NHC/graph.json","events_json":"https://pith.science/api/pith-number/QGJ5F7D2UUG4V344BGH72D2NHC/events.json","paper":"https://pith.science/paper/QGJ5F7D2"},"agent_actions":{"view_html":"https://pith.science/pith/QGJ5F7D2UUG4V344BGH72D2NHC","download_json":"https://pith.science/pith/QGJ5F7D2UUG4V344BGH72D2NHC.json","view_paper":"https://pith.science/paper/QGJ5F7D2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.7390&json=true","fetch_graph":"https://pith.science/api/pith-number/QGJ5F7D2UUG4V344BGH72D2NHC/graph.json","fetch_events":"https://pith.science/api/pith-number/QGJ5F7D2UUG4V344BGH72D2NHC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QGJ5F7D2UUG4V344BGH72D2NHC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QGJ5F7D2UUG4V344BGH72D2NHC/action/storage_attestation","attest_author":"https://pith.science/pith/QGJ5F7D2UUG4V344BGH72D2NHC/action/author_attestation","sign_citation":"https://pith.science/pith/QGJ5F7D2UUG4V344BGH72D2NHC/action/citation_signature","submit_replication":"https://pith.science/pith/QGJ5F7D2UUG4V344BGH72D2NHC/action/replication_record"}},"created_at":"2026-05-18T03:35:00.074997+00:00","updated_at":"2026-05-18T03:35:00.074997+00:00"}