{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TDWHKPZOYVHIXJVA3YN4LEGAVS","short_pith_number":"pith:TDWHKPZO","schema_version":"1.0","canonical_sha256":"98ec753f2ec54e8ba6a0de1bc590c0acb1eb36f849535ab462b4a27d0263e250","source":{"kind":"arxiv","id":"1101.3229","version":2},"attestation_state":"computed","paper":{"title":"Sparse single-index model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"CREST), DMA), G\\'erard Biau (LPMA, LSTA, Pierre Alquier (LPMA","submitted_at":"2011-01-17T14:36:55Z","abstract_excerpt":"Let $(\\bX, Y)$ be a random pair taking values in $\\mathbb R^p \\times \\mathbb R$. In the so-called single-index model, one has $Y=f^{\\star}(\\theta^{\\star T}\\bX)+\\bW$, where $f^{\\star}$ is an unknown univariate measurable function, $\\theta^{\\star}$ is an unknown vector in $\\mathbb R^d$, and $W$ denotes a random noise satisfying $\\mathbb E[\\bW|\\bX]=0$. The single-index model is known to offer a flexible way to model a variety of high-dimensional real-world phenomena. However, despite its relative simplicity, this dimension reduction scheme is faced with severe complications as soon as the underly"},"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":"1101.3229","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-01-17T14:36:55Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"4165998536b7ffd440785d50a9d85ad6ed6dab5f0235e7ff361e6594e0145cb6","abstract_canon_sha256":"96330ef0001e8d80adf09322c2dc1083636e1a0f6e43ce1efbe8e914f4711ac1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:57.269871Z","signature_b64":"6COmEcwytY67Y4/cY+SjFDlu+vU0c0sYJJk7yP1cEab9UqRoJFE+vLS3/hgKP16Yp5Bk6zlIybIADcQHkQ1EBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98ec753f2ec54e8ba6a0de1bc590c0acb1eb36f849535ab462b4a27d0263e250","last_reissued_at":"2026-05-18T03:20:57.269217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:57.269217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sparse single-index model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"CREST), DMA), G\\'erard Biau (LPMA, LSTA, Pierre Alquier (LPMA","submitted_at":"2011-01-17T14:36:55Z","abstract_excerpt":"Let $(\\bX, Y)$ be a random pair taking values in $\\mathbb R^p \\times \\mathbb R$. In the so-called single-index model, one has $Y=f^{\\star}(\\theta^{\\star T}\\bX)+\\bW$, where $f^{\\star}$ is an unknown univariate measurable function, $\\theta^{\\star}$ is an unknown vector in $\\mathbb R^d$, and $W$ denotes a random noise satisfying $\\mathbb E[\\bW|\\bX]=0$. The single-index model is known to offer a flexible way to model a variety of high-dimensional real-world phenomena. However, despite its relative simplicity, this dimension reduction scheme is faced with severe complications as soon as the underly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3229","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":"1101.3229","created_at":"2026-05-18T03:20:57.269334+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.3229v2","created_at":"2026-05-18T03:20:57.269334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3229","created_at":"2026-05-18T03:20:57.269334+00:00"},{"alias_kind":"pith_short_12","alias_value":"TDWHKPZOYVHI","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TDWHKPZOYVHIXJVA","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TDWHKPZO","created_at":"2026-05-18T12:26:42.757692+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/TDWHKPZOYVHIXJVA3YN4LEGAVS","json":"https://pith.science/pith/TDWHKPZOYVHIXJVA3YN4LEGAVS.json","graph_json":"https://pith.science/api/pith-number/TDWHKPZOYVHIXJVA3YN4LEGAVS/graph.json","events_json":"https://pith.science/api/pith-number/TDWHKPZOYVHIXJVA3YN4LEGAVS/events.json","paper":"https://pith.science/paper/TDWHKPZO"},"agent_actions":{"view_html":"https://pith.science/pith/TDWHKPZOYVHIXJVA3YN4LEGAVS","download_json":"https://pith.science/pith/TDWHKPZOYVHIXJVA3YN4LEGAVS.json","view_paper":"https://pith.science/paper/TDWHKPZO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.3229&json=true","fetch_graph":"https://pith.science/api/pith-number/TDWHKPZOYVHIXJVA3YN4LEGAVS/graph.json","fetch_events":"https://pith.science/api/pith-number/TDWHKPZOYVHIXJVA3YN4LEGAVS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TDWHKPZOYVHIXJVA3YN4LEGAVS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TDWHKPZOYVHIXJVA3YN4LEGAVS/action/storage_attestation","attest_author":"https://pith.science/pith/TDWHKPZOYVHIXJVA3YN4LEGAVS/action/author_attestation","sign_citation":"https://pith.science/pith/TDWHKPZOYVHIXJVA3YN4LEGAVS/action/citation_signature","submit_replication":"https://pith.science/pith/TDWHKPZOYVHIXJVA3YN4LEGAVS/action/replication_record"}},"created_at":"2026-05-18T03:20:57.269334+00:00","updated_at":"2026-05-18T03:20:57.269334+00:00"}