{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CMZAGVFGRGPVAGZNEYSW2STR25","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":"270361deaf096ec92270c883e469666b4da7d5f06caf850b163baf951b0ae537","cross_cats_sorted":["cs.NA","math.ST","stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-01T04:25:42Z","title_canon_sha256":"77d5491ea517b310dc156ff54219a51b472270826d4176f38f2ace10ac10900a"},"schema_version":"1.0","source":{"id":"1404.0122","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0122","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0122v2","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0122","created_at":"2026-05-18T02:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"CMZAGVFGRGPV","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CMZAGVFGRGPVAGZN","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CMZAGVFG","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:ee177cc1af5cca5aad8af4478a27406b02435a200e056582226b2f12a1fdc771","target":"graph","created_at":"2026-05-18T02:28:47Z","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":"This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where the uncertainties in the major stochastic steps are quantified. Such stochastic steps involve approximating the NLS objective function using Monte-Carlo methods, and this is equivalent to the estimation of the trace of corresponding symmetric positive semi-definite (SPSD) matrices. For the latter, we prove tight necessary and sufficient conditions on the sam","authors_text":"Farbod Roosta-Khorasani, G\\'abor J. Sz\\'ekely, Uri Ascher","cross_cats":["cs.NA","math.ST","stat.AP","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-01T04:25:42Z","title":"Assessing stochastic algorithms for large scale nonlinear least squares problems using extremal probabilities of linear combinations of gamma random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0122","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":"sha256:60137feeb77a2f190be6fa38a60fcf0a73e549b8cfffd1f22b5f9cc0a3680320","target":"record","created_at":"2026-05-18T02:28:47Z","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":"270361deaf096ec92270c883e469666b4da7d5f06caf850b163baf951b0ae537","cross_cats_sorted":["cs.NA","math.ST","stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-04-01T04:25:42Z","title_canon_sha256":"77d5491ea517b310dc156ff54219a51b472270826d4176f38f2ace10ac10900a"},"schema_version":"1.0","source":{"id":"1404.0122","kind":"arxiv","version":2}},"canonical_sha256":"13320354a6899f501b2d26256d4a71d7665dfecdaf430c8d68e5c2b22e670b00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13320354a6899f501b2d26256d4a71d7665dfecdaf430c8d68e5c2b22e670b00","first_computed_at":"2026-05-18T02:28:47.977292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:47.977292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SdwCpNLvrT4+7fZz/xX8hT2DCauVmk482zfDAsXRgzQgfKN+SLRtb9mL5irpsMoYEdLSnB32/8fFaA+qZdTmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:47.977721Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0122","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60137feeb77a2f190be6fa38a60fcf0a73e549b8cfffd1f22b5f9cc0a3680320","sha256:ee177cc1af5cca5aad8af4478a27406b02435a200e056582226b2f12a1fdc771"],"state_sha256":"cab489a135d1dbacb0f65221dffed5635c1b0ee790c3feb827935dea01a54d12"}