{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FHDHMIOK5TUJQAZY2MZKZD6RBX","short_pith_number":"pith:FHDHMIOK","schema_version":"1.0","canonical_sha256":"29c67621caece8980338d332ac8fd10df9a4b332cb99e89f6ab69fb09f85379d","source":{"kind":"arxiv","id":"1709.00127","version":1},"attestation_state":"computed","paper":{"title":"Low Permutation-rank Matrices: Structural Properties and Noisy Completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"stat.ML","authors_text":"Martin J. Wainwright, Nihar B. Shah, Sivaraman Balakrishnan","submitted_at":"2017-09-01T01:25:45Z","abstract_excerpt":"We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming that the underlying matrix has low rank, or is well-approximated by a low rank matrix. In this paper, we propose a richer model based on what we term the \"permutation-rank\" of a matrix. We first describe how the classical non-negative rank model enforces restrictions that may be undesirable in practice, and how and these restrictions can be avoided by using 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":"1709.00127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-09-01T01:25:45Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"title_canon_sha256":"c2fc5da3bf49a911df50b0ceae4106b3f084df72c2c727145667f0651f28b711","abstract_canon_sha256":"036ffb7318c32d03cf8dca5970baefeddd6a1df339e2a05b319f29aea0c18e1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:13.336069Z","signature_b64":"js/m4PAppdKiMPEii/8YfvwUA+rJM4GBOFr2FT42T1N2poiV1xPKUg9ZbMj36HKthUuWOB1kTeQvOao/eVX3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29c67621caece8980338d332ac8fd10df9a4b332cb99e89f6ab69fb09f85379d","last_reissued_at":"2026-05-18T00:36:13.335093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:13.335093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low Permutation-rank Matrices: Structural Properties and Noisy Completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"stat.ML","authors_text":"Martin J. Wainwright, Nihar B. Shah, Sivaraman Balakrishnan","submitted_at":"2017-09-01T01:25:45Z","abstract_excerpt":"We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming that the underlying matrix has low rank, or is well-approximated by a low rank matrix. In this paper, we propose a richer model based on what we term the \"permutation-rank\" of a matrix. We first describe how the classical non-negative rank model enforces restrictions that may be undesirable in practice, and how and these restrictions can be avoided by using the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00127","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":"1709.00127","created_at":"2026-05-18T00:36:13.335252+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.00127v1","created_at":"2026-05-18T00:36:13.335252+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00127","created_at":"2026-05-18T00:36:13.335252+00:00"},{"alias_kind":"pith_short_12","alias_value":"FHDHMIOK5TUJ","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FHDHMIOK5TUJQAZY","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FHDHMIOK","created_at":"2026-05-18T12:31:15.632608+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.16615","citing_title":"Learning What Evaluators Value: A Reliable Approach to Modeling Evaluator Preferences","ref_index":74,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FHDHMIOK5TUJQAZY2MZKZD6RBX","json":"https://pith.science/pith/FHDHMIOK5TUJQAZY2MZKZD6RBX.json","graph_json":"https://pith.science/api/pith-number/FHDHMIOK5TUJQAZY2MZKZD6RBX/graph.json","events_json":"https://pith.science/api/pith-number/FHDHMIOK5TUJQAZY2MZKZD6RBX/events.json","paper":"https://pith.science/paper/FHDHMIOK"},"agent_actions":{"view_html":"https://pith.science/pith/FHDHMIOK5TUJQAZY2MZKZD6RBX","download_json":"https://pith.science/pith/FHDHMIOK5TUJQAZY2MZKZD6RBX.json","view_paper":"https://pith.science/paper/FHDHMIOK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.00127&json=true","fetch_graph":"https://pith.science/api/pith-number/FHDHMIOK5TUJQAZY2MZKZD6RBX/graph.json","fetch_events":"https://pith.science/api/pith-number/FHDHMIOK5TUJQAZY2MZKZD6RBX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FHDHMIOK5TUJQAZY2MZKZD6RBX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FHDHMIOK5TUJQAZY2MZKZD6RBX/action/storage_attestation","attest_author":"https://pith.science/pith/FHDHMIOK5TUJQAZY2MZKZD6RBX/action/author_attestation","sign_citation":"https://pith.science/pith/FHDHMIOK5TUJQAZY2MZKZD6RBX/action/citation_signature","submit_replication":"https://pith.science/pith/FHDHMIOK5TUJQAZY2MZKZD6RBX/action/replication_record"}},"created_at":"2026-05-18T00:36:13.335252+00:00","updated_at":"2026-05-18T00:36:13.335252+00:00"}