{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UZCOCY4MQFNS7IZAARUECBCU6X","short_pith_number":"pith:UZCOCY4M","canonical_record":{"source":{"id":"1802.06967","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-02-20T04:52:26Z","cross_cats_sorted":[],"title_canon_sha256":"7943613d35ad64a32e26d478520fc88ce3727c0c4a19a4da351f8165697f48a9","abstract_canon_sha256":"378933b189ad476bac1c2c0af91e1476ba7b6944d6b48ea6af2c4d8c488ef9b7"},"schema_version":"1.0"},"canonical_sha256":"a644e1638c815b2fa3200468410454f5ce038b77bfab0b3958a443dd0e1992af","source":{"kind":"arxiv","id":"1802.06967","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06967","created_at":"2026-05-17T23:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06967v2","created_at":"2026-05-17T23:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06967","created_at":"2026-05-17T23:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"UZCOCY4MQFNS","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UZCOCY4MQFNS7IZA","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UZCOCY4M","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UZCOCY4MQFNS7IZAARUECBCU6X","target":"record","payload":{"canonical_record":{"source":{"id":"1802.06967","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-02-20T04:52:26Z","cross_cats_sorted":[],"title_canon_sha256":"7943613d35ad64a32e26d478520fc88ce3727c0c4a19a4da351f8165697f48a9","abstract_canon_sha256":"378933b189ad476bac1c2c0af91e1476ba7b6944d6b48ea6af2c4d8c488ef9b7"},"schema_version":"1.0"},"canonical_sha256":"a644e1638c815b2fa3200468410454f5ce038b77bfab0b3958a443dd0e1992af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:55.674484Z","signature_b64":"JMwNBiLryL2z05u36RxPh+bzdple0VI10BDHoq7cKHh+ettPSMsgSqtvlJB/b07FTIzasgpTEup0ezOcInpKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a644e1638c815b2fa3200468410454f5ce038b77bfab0b3958a443dd0e1992af","last_reissued_at":"2026-05-17T23:48:55.673749Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:55.673749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.06967","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AqDRl+KVcB/HOb50DMvefp1UoIVf0AWXLJae8Iqlpq23z3OqJ959zIbJGdo0XhJvNxCChjduytcg4ByxsSPrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:07:01.894718Z"},"content_sha256":"4e279ede6e4d50af2e0c9627aa43a34dbfbc2fc2851c9ec45c145a91a3a560ed","schema_version":"1.0","event_id":"sha256:4e279ede6e4d50af2e0c9627aa43a34dbfbc2fc2851c9ec45c145a91a3a560ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UZCOCY4MQFNS7IZAARUECBCU6X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recovery of simultaneous low rank and two-way sparse coefficient matrices, a nonconvex approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Ming Yu, Mladen Kolar, Varun Gupta","submitted_at":"2018-02-20T04:52:26Z","abstract_excerpt":"We study the problem of recovery of matrices that are simultaneously low rank and row and/or column sparse. Such matrices appear in recent applications in cognitive neuroscience, imaging, computer vision, macroeconomics, and genetics. We propose a GDT (Gradient Descent with hard Thresholding) algorithm to efficiently recover matrices with such structure, by minimizing a bi-convex function over a nonconvex set of constraints. We show linear convergence of the iterates obtained by GDT to a region within statistical error of an optimal solution. As an application of our method, we consider multi-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06967","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4T8nVCva8BG27zZpV1+2irqfNNGSl4W9sAAoWQZs6FiIR2A6Rzrgia8LC0cEzWXtViPD4gjvjv5aa4dqbzwxBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:07:01.895254Z"},"content_sha256":"8476d947cce650058679178e5e0ae89add3c3ef019e92c49e778620dc9341994","schema_version":"1.0","event_id":"sha256:8476d947cce650058679178e5e0ae89add3c3ef019e92c49e778620dc9341994"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UZCOCY4MQFNS7IZAARUECBCU6X/bundle.json","state_url":"https://pith.science/pith/UZCOCY4MQFNS7IZAARUECBCU6X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UZCOCY4MQFNS7IZAARUECBCU6X/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T18:07:01Z","links":{"resolver":"https://pith.science/pith/UZCOCY4MQFNS7IZAARUECBCU6X","bundle":"https://pith.science/pith/UZCOCY4MQFNS7IZAARUECBCU6X/bundle.json","state":"https://pith.science/pith/UZCOCY4MQFNS7IZAARUECBCU6X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UZCOCY4MQFNS7IZAARUECBCU6X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UZCOCY4MQFNS7IZAARUECBCU6X","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"378933b189ad476bac1c2c0af91e1476ba7b6944d6b48ea6af2c4d8c488ef9b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-02-20T04:52:26Z","title_canon_sha256":"7943613d35ad64a32e26d478520fc88ce3727c0c4a19a4da351f8165697f48a9"},"schema_version":"1.0","source":{"id":"1802.06967","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.06967","created_at":"2026-05-17T23:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1802.06967v2","created_at":"2026-05-17T23:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06967","created_at":"2026-05-17T23:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"UZCOCY4MQFNS","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UZCOCY4MQFNS7IZA","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UZCOCY4M","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:8476d947cce650058679178e5e0ae89add3c3ef019e92c49e778620dc9341994","target":"graph","created_at":"2026-05-17T23:48:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the problem of recovery of matrices that are simultaneously low rank and row and/or column sparse. Such matrices appear in recent applications in cognitive neuroscience, imaging, computer vision, macroeconomics, and genetics. We propose a GDT (Gradient Descent with hard Thresholding) algorithm to efficiently recover matrices with such structure, by minimizing a bi-convex function over a nonconvex set of constraints. We show linear convergence of the iterates obtained by GDT to a region within statistical error of an optimal solution. As an application of our method, we consider multi-","authors_text":"Ming Yu, Mladen Kolar, Varun Gupta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-02-20T04:52:26Z","title":"Recovery of simultaneous low rank and two-way sparse coefficient matrices, a nonconvex approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06967","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4e279ede6e4d50af2e0c9627aa43a34dbfbc2fc2851c9ec45c145a91a3a560ed","target":"record","created_at":"2026-05-17T23:48:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"378933b189ad476bac1c2c0af91e1476ba7b6944d6b48ea6af2c4d8c488ef9b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-02-20T04:52:26Z","title_canon_sha256":"7943613d35ad64a32e26d478520fc88ce3727c0c4a19a4da351f8165697f48a9"},"schema_version":"1.0","source":{"id":"1802.06967","kind":"arxiv","version":2}},"canonical_sha256":"a644e1638c815b2fa3200468410454f5ce038b77bfab0b3958a443dd0e1992af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a644e1638c815b2fa3200468410454f5ce038b77bfab0b3958a443dd0e1992af","first_computed_at":"2026-05-17T23:48:55.673749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:55.673749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JMwNBiLryL2z05u36RxPh+bzdple0VI10BDHoq7cKHh+ettPSMsgSqtvlJB/b07FTIzasgpTEup0ezOcInpKBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:55.674484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.06967","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e279ede6e4d50af2e0c9627aa43a34dbfbc2fc2851c9ec45c145a91a3a560ed","sha256:8476d947cce650058679178e5e0ae89add3c3ef019e92c49e778620dc9341994"],"state_sha256":"ae2f4e7cc87d4bcd463d0a0a8bfa58bba46dc265b9e332d654dd1bf7377b7dc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xocBAcZ07J5Cbg+UByBT3T1N8QT3eOgnrIxzgdW3EZ0bqsCziTNNgexyhb9i9US2UnMtR4gyNuNJ8ZvGCmM5Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:07:01.898398Z","bundle_sha256":"6e062033a513d6171b93f194d3fd6d3da54f2045d30522f68db3a0bde0d8253b"}}