{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OQIPUKUNWT26XYB4OEWJJ4ASTI","short_pith_number":"pith:OQIPUKUN","schema_version":"1.0","canonical_sha256":"7410fa2a8db4f5ebe03c712c94f0129a2b6c2011c459c5896e64a77a271d7345","source":{"kind":"arxiv","id":"1305.0030","version":2},"attestation_state":"computed","paper":{"title":"A least-squares method for sparse low rank approximation of multivariate functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.NA","authors_text":"Anthony Nouy, Mathilde Chevreuil, Prashant Rai, R\\'egis Lebrun","submitted_at":"2013-04-30T21:25:54Z","abstract_excerpt":"In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within classical algorithms for low-rank approximation in order to exploit the possible sparsity of low-rank approximations. Sparse low-rank approximations are constructed with a robust updated greedy algorithm which includes an optimal selection of regularization parameters and approximation ranks using cross validation techniques. Numerical examples demonstrate the "},"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":"1305.0030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-04-30T21:25:54Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"8cb31a02bd2843d0f068b4f4395c1be87413df4407262cfecbf0a6a143572b27","abstract_canon_sha256":"983bb47ce43a21efd8741e6197fa9919a29bb04d4deed1c69875c73a57fd01e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:08.939442Z","signature_b64":"n4BWVC3JYG9Lj1od4vx0qsFZwcM2X7d8O5GFDRYuxIG4hTvwngDzV0jzS8YnvlRPvAtYOQzSzPjTq1ygQIFDBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7410fa2a8db4f5ebe03c712c94f0129a2b6c2011c459c5896e64a77a271d7345","last_reissued_at":"2026-05-18T01:25:08.938954Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:08.938954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A least-squares method for sparse low rank approximation of multivariate functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.NA","authors_text":"Anthony Nouy, Mathilde Chevreuil, Prashant Rai, R\\'egis Lebrun","submitted_at":"2013-04-30T21:25:54Z","abstract_excerpt":"In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within classical algorithms for low-rank approximation in order to exploit the possible sparsity of low-rank approximations. Sparse low-rank approximations are constructed with a robust updated greedy algorithm which includes an optimal selection of regularization parameters and approximation ranks using cross validation techniques. Numerical examples demonstrate the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0030","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":"1305.0030","created_at":"2026-05-18T01:25:08.939022+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0030v2","created_at":"2026-05-18T01:25:08.939022+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0030","created_at":"2026-05-18T01:25:08.939022+00:00"},{"alias_kind":"pith_short_12","alias_value":"OQIPUKUNWT26","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OQIPUKUNWT26XYB4","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OQIPUKUN","created_at":"2026-05-18T12:27:54.935989+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/OQIPUKUNWT26XYB4OEWJJ4ASTI","json":"https://pith.science/pith/OQIPUKUNWT26XYB4OEWJJ4ASTI.json","graph_json":"https://pith.science/api/pith-number/OQIPUKUNWT26XYB4OEWJJ4ASTI/graph.json","events_json":"https://pith.science/api/pith-number/OQIPUKUNWT26XYB4OEWJJ4ASTI/events.json","paper":"https://pith.science/paper/OQIPUKUN"},"agent_actions":{"view_html":"https://pith.science/pith/OQIPUKUNWT26XYB4OEWJJ4ASTI","download_json":"https://pith.science/pith/OQIPUKUNWT26XYB4OEWJJ4ASTI.json","view_paper":"https://pith.science/paper/OQIPUKUN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0030&json=true","fetch_graph":"https://pith.science/api/pith-number/OQIPUKUNWT26XYB4OEWJJ4ASTI/graph.json","fetch_events":"https://pith.science/api/pith-number/OQIPUKUNWT26XYB4OEWJJ4ASTI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OQIPUKUNWT26XYB4OEWJJ4ASTI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OQIPUKUNWT26XYB4OEWJJ4ASTI/action/storage_attestation","attest_author":"https://pith.science/pith/OQIPUKUNWT26XYB4OEWJJ4ASTI/action/author_attestation","sign_citation":"https://pith.science/pith/OQIPUKUNWT26XYB4OEWJJ4ASTI/action/citation_signature","submit_replication":"https://pith.science/pith/OQIPUKUNWT26XYB4OEWJJ4ASTI/action/replication_record"}},"created_at":"2026-05-18T01:25:08.939022+00:00","updated_at":"2026-05-18T01:25:08.939022+00:00"}