{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HYVPIBC4CEO2XNGYDKQ34YYSAT","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":"cfcac993e522afb0a21029848aac27e76f0e86689a9810be4bc71808aafc1390","cross_cats_sorted":["cs.LG","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-10T12:21:47Z","title_canon_sha256":"2977192a6c549fa9a5cbf5a7556a7445b23220a07c0c228cc81c0385b24819b1"},"schema_version":"1.0","source":{"id":"1808.03504","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03504","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03504v1","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03504","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"HYVPIBC4CEO2","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HYVPIBC4CEO2XNGY","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HYVPIBC4","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:3179b4387a680cb48cdd8cd699624ccc5e5f6a9a7903c68d61dd74ceae8ffb17","target":"graph","created_at":"2026-05-18T00:08:24Z","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":"In this paper, we present a general, multistage framework for graphical model approximation using a cascade of models such as trees. In particular, we look at the problem of covariance matrix approximation for Gaussian distributions as linear transformations of tree models. This is a new way to decompose the covariance matrix. Here, we propose an algorithm which incorporates the Cholesky factorization method to compute the decomposition matrix and thus can approximate a simple graphical model using a cascade of the Cholesky factorization of the tree approximation transformations. The Cholesky ","authors_text":"Anthony Kuh, Navid Tafaghodi Khajavi","cross_cats":["cs.LG","math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-10T12:21:47Z","title":"Model Approximation Using Cascade of Tree Decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03504","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:f7bd45d2f313630b53a5d1e7bbf229ac3ed79c9bc7a40c518054b49b1b718320","target":"record","created_at":"2026-05-18T00:08:24Z","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":"cfcac993e522afb0a21029848aac27e76f0e86689a9810be4bc71808aafc1390","cross_cats_sorted":["cs.LG","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-10T12:21:47Z","title_canon_sha256":"2977192a6c549fa9a5cbf5a7556a7445b23220a07c0c228cc81c0385b24819b1"},"schema_version":"1.0","source":{"id":"1808.03504","kind":"arxiv","version":1}},"canonical_sha256":"3e2af4045c111dabb4d81aa1be631204e8189aeeb3f8c6903c0388aa0687a912","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e2af4045c111dabb4d81aa1be631204e8189aeeb3f8c6903c0388aa0687a912","first_computed_at":"2026-05-18T00:08:24.839675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:24.839675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r4oWCbmFBxm4XpF3xq1TeYw4ceA3GQtMt0SwY3d4aAXpc4fWUM4Vu76+dFViEjen5gQbwIsHqskrCbJoe0bqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:24.840283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.03504","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7bd45d2f313630b53a5d1e7bbf229ac3ed79c9bc7a40c518054b49b1b718320","sha256:3179b4387a680cb48cdd8cd699624ccc5e5f6a9a7903c68d61dd74ceae8ffb17"],"state_sha256":"94b0f69aa67f9e80511fe42645cebf4d008d0e09ad5b19956c9e4d5545d913c4"}