{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XRJBWEDS4SBWS6MWWQW4BUNK2M","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":"ebcfddac32358802f0a9276aa2daa25e319c323f3c9989017365c5d636dd331a","cross_cats_sorted":["cs.IT","cs.LG","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-03T02:59:39Z","title_canon_sha256":"9046622e27927c1a1c343eed3c4d9f80d02f53a1fcc849b6e07a4d527d328222"},"schema_version":"1.0","source":{"id":"1411.0347","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0347","created_at":"2026-05-18T02:38:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0347v1","created_at":"2026-05-18T02:38:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0347","created_at":"2026-05-18T02:38:51Z"},{"alias_kind":"pith_short_12","alias_value":"XRJBWEDS4SBW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XRJBWEDS4SBWS6MW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XRJBWEDS","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:9d2147b3f30a71f8ab2982b40d677701a9f9a31a031213f9c69576a4eee946ce","target":"graph","created_at":"2026-05-18T02:38:51Z","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 randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the quadratic objective function (cost approximation), or in terms of some distance measure between the approximate minimizer and the true minimizer (solution approximation). Focusing on the latter criterion, our first main result provides a general lower bound on any randomized method that sketches both the data matrix and vector in a least-squares problem; as a su","authors_text":"Martin J. Wainwright, Mert Pilanci","cross_cats":["cs.IT","cs.LG","math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-03T02:59:39Z","title":"Iterative Hessian sketch: Fast and accurate solution approximation for constrained least-squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0347","kind":"arxiv","version":1},"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":"sha256:385308d280ccb5c727cbfb3797c79da024ec7dc2d48399b0ff623760d021ef0e","target":"record","created_at":"2026-05-18T02:38:51Z","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":"ebcfddac32358802f0a9276aa2daa25e319c323f3c9989017365c5d636dd331a","cross_cats_sorted":["cs.IT","cs.LG","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-03T02:59:39Z","title_canon_sha256":"9046622e27927c1a1c343eed3c4d9f80d02f53a1fcc849b6e07a4d527d328222"},"schema_version":"1.0","source":{"id":"1411.0347","kind":"arxiv","version":1}},"canonical_sha256":"bc521b1072e483697996b42dc0d1aad315681013b048166ac8d2774df008ce7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc521b1072e483697996b42dc0d1aad315681013b048166ac8d2774df008ce7c","first_computed_at":"2026-05-18T02:38:51.943839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:51.943839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cJ7vUF2VWbkV2uOjFrnOoVqyZsO7NM3/MxvoXB1F8+R6ebeFDrPMtJsNzMeL28d99m/uh17Z/FiuNBcBpozJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:51.944349Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0347","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:385308d280ccb5c727cbfb3797c79da024ec7dc2d48399b0ff623760d021ef0e","sha256:9d2147b3f30a71f8ab2982b40d677701a9f9a31a031213f9c69576a4eee946ce"],"state_sha256":"225575ba2ea0dd824f543eeb8e87db7fd9f54aa966944cda43561a80b3528833"}