{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:V2ROQFFRS5L3ERVLHFFKWCEFDJ","short_pith_number":"pith:V2ROQFFR","canonical_record":{"source":{"id":"1402.5131","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-02-20T20:48:10Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"4b712bd685f53cbe6968caf7d32202d1743cac85399fa988371feef1e672f5bb","abstract_canon_sha256":"f01f621d4a0a949176535de225862ecb5df47498cf19d14ac8fb1a3439587a63"},"schema_version":"1.0"},"canonical_sha256":"aea2e814b19757b246ab394aab08851a730336ba8dcd3d2623654e31ec2fea56","source":{"kind":"arxiv","id":"1402.5131","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5131","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5131v6","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5131","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"pith_short_12","alias_value":"V2ROQFFRS5L3","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V2ROQFFRS5L3ERVL","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V2ROQFFR","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:V2ROQFFRS5L3ERVLHFFKWCEFDJ","target":"record","payload":{"canonical_record":{"source":{"id":"1402.5131","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-02-20T20:48:10Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"4b712bd685f53cbe6968caf7d32202d1743cac85399fa988371feef1e672f5bb","abstract_canon_sha256":"f01f621d4a0a949176535de225862ecb5df47498cf19d14ac8fb1a3439587a63"},"schema_version":"1.0"},"canonical_sha256":"aea2e814b19757b246ab394aab08851a730336ba8dcd3d2623654e31ec2fea56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:16.237874Z","signature_b64":"/H7oc8IO3uImswIQkc1XKsYS0zYSa/wEZKyJFkXIN4MHEwN/ud2QZIYKCIO7PYSQDnBNGhj5oWJUvFH/lpgLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aea2e814b19757b246ab394aab08851a730336ba8dcd3d2623654e31ec2fea56","last_reissued_at":"2026-05-18T01:37:16.237124Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:16.237124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.5131","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5w/f9gA5WhNJXIUiy6HvIDuTuwqTj0lvFMSVntFOWxvKw+MQnI0UpcVIAVWU+JchaIgAtvUH2aq5SGBXn+bdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:37:13.007261Z"},"content_sha256":"8f7527986da70b5c0d4ab488c8c30c2a4896b12a2f843b791fbea6bcb0f66f5e","schema_version":"1.0","event_id":"sha256:8f7527986da70b5c0d4ab488c8c30c2a4896b12a2f843b791fbea6bcb0f66f5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:V2ROQFFRS5L3ERVLHFFKWCEFDJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Step Stochastic ADMM in High Dimensions: Applications to Sparse Optimization and Noisy Matrix Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Anima Anandkumar, Edmond Jonckheere, Hanie Sedghi","submitted_at":"2014-02-20T20:48:10Z","abstract_excerpt":"We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the modified ADMM method has an optimal convergence rate of $\\mathcal{O}(s\\log d/T)$, where $s$ is the sparsity level, $d$ is the data dimension and $T$ is the number of steps. This matches with the minimax lower bounds for sparse estimation. For matrix decomposition into sparse and low rank components, we provide the first guarantees for any online method, and pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5131","kind":"arxiv","version":6},"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":"2026-05-18T01:37:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OcCAOGiUVF3V9zsSKjTIXDOjLgqG2kz+9NucUtrz8sZaUa0RC0JvL5WmA4oU6wps9Ts4mp0AvUGbVYS97qdgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:37:13.007630Z"},"content_sha256":"fcfb42833cb9e2d7fcda07edd4ef31ae7a7b5939536c084c76389518a53315e1","schema_version":"1.0","event_id":"sha256:fcfb42833cb9e2d7fcda07edd4ef31ae7a7b5939536c084c76389518a53315e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V2ROQFFRS5L3ERVLHFFKWCEFDJ/bundle.json","state_url":"https://pith.science/pith/V2ROQFFRS5L3ERVLHFFKWCEFDJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V2ROQFFRS5L3ERVLHFFKWCEFDJ/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":"2026-06-03T04:37:13Z","links":{"resolver":"https://pith.science/pith/V2ROQFFRS5L3ERVLHFFKWCEFDJ","bundle":"https://pith.science/pith/V2ROQFFRS5L3ERVLHFFKWCEFDJ/bundle.json","state":"https://pith.science/pith/V2ROQFFRS5L3ERVLHFFKWCEFDJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V2ROQFFRS5L3ERVLHFFKWCEFDJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:V2ROQFFRS5L3ERVLHFFKWCEFDJ","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":"f01f621d4a0a949176535de225862ecb5df47498cf19d14ac8fb1a3439587a63","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-02-20T20:48:10Z","title_canon_sha256":"4b712bd685f53cbe6968caf7d32202d1743cac85399fa988371feef1e672f5bb"},"schema_version":"1.0","source":{"id":"1402.5131","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5131","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5131v6","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5131","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"pith_short_12","alias_value":"V2ROQFFRS5L3","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V2ROQFFRS5L3ERVL","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V2ROQFFR","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:fcfb42833cb9e2d7fcda07edd4ef31ae7a7b5939536c084c76389518a53315e1","target":"graph","created_at":"2026-05-18T01:37:16Z","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 propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the modified ADMM method has an optimal convergence rate of $\\mathcal{O}(s\\log d/T)$, where $s$ is the sparsity level, $d$ is the data dimension and $T$ is the number of steps. This matches with the minimax lower bounds for sparse estimation. For matrix decomposition into sparse and low rank components, we provide the first guarantees for any online method, and pro","authors_text":"Anima Anandkumar, Edmond Jonckheere, Hanie Sedghi","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-02-20T20:48:10Z","title":"Multi-Step Stochastic ADMM in High Dimensions: Applications to Sparse Optimization and Noisy Matrix Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5131","kind":"arxiv","version":6},"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":"sha256:8f7527986da70b5c0d4ab488c8c30c2a4896b12a2f843b791fbea6bcb0f66f5e","target":"record","created_at":"2026-05-18T01:37:16Z","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":"f01f621d4a0a949176535de225862ecb5df47498cf19d14ac8fb1a3439587a63","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-02-20T20:48:10Z","title_canon_sha256":"4b712bd685f53cbe6968caf7d32202d1743cac85399fa988371feef1e672f5bb"},"schema_version":"1.0","source":{"id":"1402.5131","kind":"arxiv","version":6}},"canonical_sha256":"aea2e814b19757b246ab394aab08851a730336ba8dcd3d2623654e31ec2fea56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aea2e814b19757b246ab394aab08851a730336ba8dcd3d2623654e31ec2fea56","first_computed_at":"2026-05-18T01:37:16.237124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:16.237124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/H7oc8IO3uImswIQkc1XKsYS0zYSa/wEZKyJFkXIN4MHEwN/ud2QZIYKCIO7PYSQDnBNGhj5oWJUvFH/lpgLCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:16.237874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5131","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f7527986da70b5c0d4ab488c8c30c2a4896b12a2f843b791fbea6bcb0f66f5e","sha256:fcfb42833cb9e2d7fcda07edd4ef31ae7a7b5939536c084c76389518a53315e1"],"state_sha256":"7f435bc5b97a0a420bf7eaa6664b8b4a3735517a890275025668cbe55dbc7213"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yn8fWaIdF+SM1NQxXHz7tAyrFGL5VRnQw/v9xrKFclorO1lWSi7RyBUahkJ2yNMnTExevHSbjNpgentnsaO9Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T04:37:13.009658Z","bundle_sha256":"855458dd5e819cb1e37437923ca8d882937d22ac0ea230d98e0ea89da44c64a6"}}