{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EYQD2BMAZ2767H4C5ZJ7AJRN4F","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":"2600615dca38d638f028fa084647a1a5605f5e990f06048f15177e82370edf58","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2011-12-20T12:59:09Z","title_canon_sha256":"55cc3908bc23a79582a8eff004c2f37eff91fb477d3715bce6954cfd1cca3640"},"schema_version":"1.0","source":{"id":"1112.4675","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4675","created_at":"2026-05-18T02:51:15Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4675v2","created_at":"2026-05-18T02:51:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4675","created_at":"2026-05-18T02:51:15Z"},{"alias_kind":"pith_short_12","alias_value":"EYQD2BMAZ276","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EYQD2BMAZ2767H4C","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EYQD2BMA","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:97f66eb14d5e3faec2451a5a9b52c18a935aa954b7c5be75c4ad6a0f416e2b3d","target":"graph","created_at":"2026-05-18T02:51:15Z","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":"Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare different mixture models using penalized log-likelihood criteria such as BIC.We propose fitting MLMMs with variational methods which can perform parameter estimation and model selection simultaneously. A variational approximation is described where the variational lower bound and parameter updates are in closed form, allowing fast evaluation. A new variation","authors_text":"David J. Nott, Siew Li Tan","cross_cats":["stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2011-12-20T12:59:09Z","title":"Variational approximation for mixtures of linear mixed models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4675","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":"sha256:85a54ae9b90d26620d3fc0e335471b0765c57f0f2637f43fd202825e8413667b","target":"record","created_at":"2026-05-18T02:51:15Z","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":"2600615dca38d638f028fa084647a1a5605f5e990f06048f15177e82370edf58","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2011-12-20T12:59:09Z","title_canon_sha256":"55cc3908bc23a79582a8eff004c2f37eff91fb477d3715bce6954cfd1cca3640"},"schema_version":"1.0","source":{"id":"1112.4675","kind":"arxiv","version":2}},"canonical_sha256":"26203d0580cebfef9f82ee53f0262de1530243338f60a67b3f243a20545af94d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26203d0580cebfef9f82ee53f0262de1530243338f60a67b3f243a20545af94d","first_computed_at":"2026-05-18T02:51:15.321359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:15.321359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hoCx27D4A5G35PHnVR6pzqXs/zNJWNWU5j2RqpxMS455gPfROZFm2JECLOfAfefLbBslqHMReGOzEkuX05NdDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:15.321826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4675","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85a54ae9b90d26620d3fc0e335471b0765c57f0f2637f43fd202825e8413667b","sha256:97f66eb14d5e3faec2451a5a9b52c18a935aa954b7c5be75c4ad6a0f416e2b3d"],"state_sha256":"723f37b80e45939b4f40040af42c8780783333c4e3a1a9e72df591f19831dfec"}