{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:S5FHAPJWUNZ3M6VQUEFJAITD57","short_pith_number":"pith:S5FHAPJW","schema_version":"1.0","canonical_sha256":"974a703d36a373b67ab0a10a902263efc948f9aa7691d1f3c695e0e33e1dc999","source":{"kind":"arxiv","id":"1408.5369","version":2},"attestation_state":"computed","paper":{"title":"Statistical and computational trade-offs in estimation of sparse principal components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Quentin Berthet, Richard J. Samworth, Tengyao Wang","submitted_at":"2014-08-22T17:42:35Z","abstract_excerpt":"In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a population covariance matrix under the assumption that this eigenvector is sparse. An impressive range of estimators have been proposed; some of these are fast to compute, while others are known to achieve the minimax optimal rate over certain Gaussian or sub-Gaussian classes. In this paper, we show that, under a widely-believed assumption from computational "},"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":"1408.5369","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-08-22T17:42:35Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"1568a9b77add4a253d9177a71377a473cf8f8344492d9c111e01439e4ec18df6","abstract_canon_sha256":"3aa93e02a34ce405f087a452e548601249fc13d3ee1cb87b8d48c997bcba327f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:44.616767Z","signature_b64":"ID8AVp7g3Z9E+doLseCi4h8r0Qg8/LHoY5tDQsudn178wXExNnE3XsO9XFOXN9QDiuo3/uoEk1s3adY+LGEhCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"974a703d36a373b67ab0a10a902263efc948f9aa7691d1f3c695e0e33e1dc999","last_reissued_at":"2026-05-18T01:03:44.616334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:44.616334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Statistical and computational trade-offs in estimation of sparse principal components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Quentin Berthet, Richard J. Samworth, Tengyao Wang","submitted_at":"2014-08-22T17:42:35Z","abstract_excerpt":"In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a population covariance matrix under the assumption that this eigenvector is sparse. An impressive range of estimators have been proposed; some of these are fast to compute, while others are known to achieve the minimax optimal rate over certain Gaussian or sub-Gaussian classes. In this paper, we show that, under a widely-believed assumption from computational "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5369","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":"1408.5369","created_at":"2026-05-18T01:03:44.616409+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.5369v2","created_at":"2026-05-18T01:03:44.616409+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5369","created_at":"2026-05-18T01:03:44.616409+00:00"},{"alias_kind":"pith_short_12","alias_value":"S5FHAPJWUNZ3","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"S5FHAPJWUNZ3M6VQ","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"S5FHAPJW","created_at":"2026-05-18T12:28:49.207871+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/S5FHAPJWUNZ3M6VQUEFJAITD57","json":"https://pith.science/pith/S5FHAPJWUNZ3M6VQUEFJAITD57.json","graph_json":"https://pith.science/api/pith-number/S5FHAPJWUNZ3M6VQUEFJAITD57/graph.json","events_json":"https://pith.science/api/pith-number/S5FHAPJWUNZ3M6VQUEFJAITD57/events.json","paper":"https://pith.science/paper/S5FHAPJW"},"agent_actions":{"view_html":"https://pith.science/pith/S5FHAPJWUNZ3M6VQUEFJAITD57","download_json":"https://pith.science/pith/S5FHAPJWUNZ3M6VQUEFJAITD57.json","view_paper":"https://pith.science/paper/S5FHAPJW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.5369&json=true","fetch_graph":"https://pith.science/api/pith-number/S5FHAPJWUNZ3M6VQUEFJAITD57/graph.json","fetch_events":"https://pith.science/api/pith-number/S5FHAPJWUNZ3M6VQUEFJAITD57/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S5FHAPJWUNZ3M6VQUEFJAITD57/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S5FHAPJWUNZ3M6VQUEFJAITD57/action/storage_attestation","attest_author":"https://pith.science/pith/S5FHAPJWUNZ3M6VQUEFJAITD57/action/author_attestation","sign_citation":"https://pith.science/pith/S5FHAPJWUNZ3M6VQUEFJAITD57/action/citation_signature","submit_replication":"https://pith.science/pith/S5FHAPJWUNZ3M6VQUEFJAITD57/action/replication_record"}},"created_at":"2026-05-18T01:03:44.616409+00:00","updated_at":"2026-05-18T01:03:44.616409+00:00"}