{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:EAFO7FGNWAWJH2NFFAJOCV4FG4","short_pith_number":"pith:EAFO7FGN","schema_version":"1.0","canonical_sha256":"200aef94cdb02c93e9a52812e15785371415affc0eafc4fb9770743aa63a769f","source":{"kind":"arxiv","id":"1408.2054","version":1},"attestation_state":"computed","paper":{"title":"Non-Convex Rank Minimization via an Empirical Bayesian Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"David Wipf","submitted_at":"2014-08-09T05:52:02Z","abstract_excerpt":"In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate penalty term for matrix rank. The problem is that in many practical scenarios there is no longer any guarantee that we can correctly estimate generative low-rank matrices of interest, theoretical special cases notwithstanding. Consequently, this paper proposes an alternative empirical Bayesian procedure build upon a variational approximation that, unlike 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":"1408.2054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-08-09T05:52:02Z","cross_cats_sorted":["cs.NA","stat.ML"],"title_canon_sha256":"c7f43816e3e967fecba12cc1e032a057ba76ab8633763668947339667db96c80","abstract_canon_sha256":"0ae0d6acd7e8faf8891b003a68432ba15a3742c3537792bd480f1240316860c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:30.512706Z","signature_b64":"vySWs2+zvFJdRckoaLnn7w00xP+zCNQXRbsX9+ue2YhJmN2OPMPOwU9+sVXYQ0gMDHxpwVrcQ1xiDVbQ0lmUBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"200aef94cdb02c93e9a52812e15785371415affc0eafc4fb9770743aa63a769f","last_reissued_at":"2026-05-18T02:45:30.512008Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:30.512008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Convex Rank Minimization via an Empirical Bayesian Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"David Wipf","submitted_at":"2014-08-09T05:52:02Z","abstract_excerpt":"In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate penalty term for matrix rank. The problem is that in many practical scenarios there is no longer any guarantee that we can correctly estimate generative low-rank matrices of interest, theoretical special cases notwithstanding. Consequently, this paper proposes an alternative empirical Bayesian procedure build upon a variational approximation that, unlike the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2054","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":"1408.2054","created_at":"2026-05-18T02:45:30.512153+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.2054v1","created_at":"2026-05-18T02:45:30.512153+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2054","created_at":"2026-05-18T02:45:30.512153+00:00"},{"alias_kind":"pith_short_12","alias_value":"EAFO7FGNWAWJ","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"EAFO7FGNWAWJH2NF","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"EAFO7FGN","created_at":"2026-05-18T12:28:25.294606+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/EAFO7FGNWAWJH2NFFAJOCV4FG4","json":"https://pith.science/pith/EAFO7FGNWAWJH2NFFAJOCV4FG4.json","graph_json":"https://pith.science/api/pith-number/EAFO7FGNWAWJH2NFFAJOCV4FG4/graph.json","events_json":"https://pith.science/api/pith-number/EAFO7FGNWAWJH2NFFAJOCV4FG4/events.json","paper":"https://pith.science/paper/EAFO7FGN"},"agent_actions":{"view_html":"https://pith.science/pith/EAFO7FGNWAWJH2NFFAJOCV4FG4","download_json":"https://pith.science/pith/EAFO7FGNWAWJH2NFFAJOCV4FG4.json","view_paper":"https://pith.science/paper/EAFO7FGN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.2054&json=true","fetch_graph":"https://pith.science/api/pith-number/EAFO7FGNWAWJH2NFFAJOCV4FG4/graph.json","fetch_events":"https://pith.science/api/pith-number/EAFO7FGNWAWJH2NFFAJOCV4FG4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EAFO7FGNWAWJH2NFFAJOCV4FG4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EAFO7FGNWAWJH2NFFAJOCV4FG4/action/storage_attestation","attest_author":"https://pith.science/pith/EAFO7FGNWAWJH2NFFAJOCV4FG4/action/author_attestation","sign_citation":"https://pith.science/pith/EAFO7FGNWAWJH2NFFAJOCV4FG4/action/citation_signature","submit_replication":"https://pith.science/pith/EAFO7FGNWAWJH2NFFAJOCV4FG4/action/replication_record"}},"created_at":"2026-05-18T02:45:30.512153+00:00","updated_at":"2026-05-18T02:45:30.512153+00:00"}