{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZLNGGLUOMK6Z45FPSG2F3S5VMK","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":"31704e52986a18817d0417e124e2a1d7af53514e20bcb2370d3d92a7779eec2f","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-27T15:28:26Z","title_canon_sha256":"a2a8eecd916df610e2081a3160a07c22fe56f347b748488835659a3844387070"},"schema_version":"1.0","source":{"id":"1412.8060","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.8060","created_at":"2026-05-18T01:49:31Z"},{"alias_kind":"arxiv_version","alias_value":"1412.8060v2","created_at":"2026-05-18T01:49:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8060","created_at":"2026-05-18T01:49:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZLNGGLUOMK6Z","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZLNGGLUOMK6Z45FP","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZLNGGLUO","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:58afaa0321382bf397078eca4fa3bf3a44764e59a9a9cf1e6012f47eb1d0622e","target":"graph","created_at":"2026-05-18T01:49:31Z","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 minimizing the sum of a smooth convex function and a convex block-separable regularizer and propose a new randomized coordinate descent method, which we call ALPHA. Our method at every iteration updates a random subset of coordinates, following an arbitrary distribution. No coordinate descent methods capable to handle an arbitrary sampling have been studied in the literature before for this problem. ALPHA is a remarkably flexible algorithm: in special cases, it reduces to deterministic and randomized methods such as gradient descent, coordinate descent, parallel coordin","authors_text":"Peter Richt\\'arik, Zheng Qu","cross_cats":["cs.LG","cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-27T15:28:26Z","title":"Coordinate Descent with Arbitrary Sampling I: Algorithms and Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8060","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":"sha256:0f837ccf3414852bc09ac11fdd641d479fc04d76b81a27f2e03091e801373887","target":"record","created_at":"2026-05-18T01:49:31Z","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":"31704e52986a18817d0417e124e2a1d7af53514e20bcb2370d3d92a7779eec2f","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-27T15:28:26Z","title_canon_sha256":"a2a8eecd916df610e2081a3160a07c22fe56f347b748488835659a3844387070"},"schema_version":"1.0","source":{"id":"1412.8060","kind":"arxiv","version":2}},"canonical_sha256":"cada632e8e62bd9e74af91b45dcbb562b1069500f8cb9bcc87bc5d5ee1cdf3ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cada632e8e62bd9e74af91b45dcbb562b1069500f8cb9bcc87bc5d5ee1cdf3ea","first_computed_at":"2026-05-18T01:49:31.328062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:31.328062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HIF5CsYluCcAwcOHHL2mL9Rx6oWRxbJoSWt6c/3nAfRRLVfnOSvShe8SRf5MkjfSyo+8uoaS8mmvozKGIbqXBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:31.328521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.8060","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f837ccf3414852bc09ac11fdd641d479fc04d76b81a27f2e03091e801373887","sha256:58afaa0321382bf397078eca4fa3bf3a44764e59a9a9cf1e6012f47eb1d0622e"],"state_sha256":"84bf79d66fda162d157cea764012364c0ea9bb6eb6296856c2ca0aff40c6c031"}