{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WRMSKKKYNLW4IEDAZ7OHRNWO2R","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":"55938dc448c5d26d2386d6d88b8d7b650f8d62dc3550d70942fda0074492e409","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2015-03-22T06:55:12Z","title_canon_sha256":"878db89d22887e0405632232445cb62ecb44931186bf5f0c7b1d4f3452118a54"},"schema_version":"1.0","source":{"id":"1503.06394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06394","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06394v1","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06394","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"pith_short_12","alias_value":"WRMSKKKYNLW4","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WRMSKKKYNLW4IEDA","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WRMSKKKY","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:a05ad3bf385e7349a26bfce17584e875d2ddd624f9fbd6b717dc4722f364f363","target":"graph","created_at":"2026-05-18T02:20:38Z","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":"Logarithms of determinants of large positive definite matrices appear ubiquitously in machine learning applications including Gaussian graphical and Gaussian process models, partition functions of discrete graphical models, minimum-volume ellipsoids, metric learning and kernel learning. Log-determinant computation involves the Cholesky decomposition at the cost cubic in the number of variables, i.e., the matrix dimension, which makes it prohibitive for large-scale applications. We propose a linear-time randomized algorithm to approximate log-determinants for very large-scale positive definite ","authors_text":"Dmitry Malioutov, Insu Han, Jinwoo Shin","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2015-03-22T06:55:12Z","title":"Large-scale Log-determinant Computation through Stochastic Chebyshev Expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06394","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":"sha256:806d5e6c52d7e4fa22f0f684f4108727fe29b62f7c2d3d511d493d663d542893","target":"record","created_at":"2026-05-18T02:20:38Z","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":"55938dc448c5d26d2386d6d88b8d7b650f8d62dc3550d70942fda0074492e409","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2015-03-22T06:55:12Z","title_canon_sha256":"878db89d22887e0405632232445cb62ecb44931186bf5f0c7b1d4f3452118a54"},"schema_version":"1.0","source":{"id":"1503.06394","kind":"arxiv","version":1}},"canonical_sha256":"b4592529586aedc41060cfdc78b6ced442165e42c890ed7243809b114d86fa13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4592529586aedc41060cfdc78b6ced442165e42c890ed7243809b114d86fa13","first_computed_at":"2026-05-18T02:20:38.542386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:38.542386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l3Er8y4X88tCm4MuUoqnXz2RhWB2RWYLvpWrUc22zlsu4Hs35Swcb/G8Ohh/g3Fzfi5ZLaCRDuwZdrgbUJkLAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:38.543039Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:806d5e6c52d7e4fa22f0f684f4108727fe29b62f7c2d3d511d493d663d542893","sha256:a05ad3bf385e7349a26bfce17584e875d2ddd624f9fbd6b717dc4722f364f363"],"state_sha256":"0f0f1e013b9c52e0ca132aa6a1aada993c6648a0fd4f3b9709b7a77ef173f4d1"}