{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:U7EKTNRTLCHXATKFJSWM646DKV","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":"6190bbb352de0c688c9e9fe415f8be2801652509a09a19962ea1274a69cdb332","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-08-02T05:20:01Z","title_canon_sha256":"11766836cc31eebde7ceaaeaf68b7efbaf4aa68e1693d0dd1ff0a194343e07dd"},"schema_version":"1.0","source":{"id":"1208.0402","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0402","created_at":"2026-05-18T03:49:34Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0402v1","created_at":"2026-05-18T03:49:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0402","created_at":"2026-05-18T03:49:34Z"},{"alias_kind":"pith_short_12","alias_value":"U7EKTNRTLCHX","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U7EKTNRTLCHXATKF","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U7EKTNRT","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:be4c061af9eabccff07de09e8ac9e6ac0b3da0b2d4462c4f47a516307159a882","target":"graph","created_at":"2026-05-18T03:49:34Z","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 present the multidimensional membership mixture (M3) models where every dimension of the membership represents an independent mixture model and each data point is generated from the selected mixture components jointly. This is helpful when the data has a certain shared structure. For example, three unique means and three unique variances can effectively form a Gaussian mixture model with nine components, while requiring only six parameters to fully describe it. In this paper, we present three instantiations of M3 models (together with the learning and inference algorithms): infinite, finite","authors_text":"Ashutosh Saxena, Marcus Lim, Yun Jiang","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-08-02T05:20:01Z","title":"Multidimensional Membership Mixture Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0402","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":"sha256:5ba812cdaf75e4ccbd12828eae78af0e5293ca0d89d1cfae01f577144b14e85d","target":"record","created_at":"2026-05-18T03:49:34Z","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":"6190bbb352de0c688c9e9fe415f8be2801652509a09a19962ea1274a69cdb332","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-08-02T05:20:01Z","title_canon_sha256":"11766836cc31eebde7ceaaeaf68b7efbaf4aa68e1693d0dd1ff0a194343e07dd"},"schema_version":"1.0","source":{"id":"1208.0402","kind":"arxiv","version":1}},"canonical_sha256":"a7c8a9b633588f704d454caccf73c3556d28fcbe88204d843e12d4b180aaef11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7c8a9b633588f704d454caccf73c3556d28fcbe88204d843e12d4b180aaef11","first_computed_at":"2026-05-18T03:49:34.287993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:34.287993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MKk3WQOoekVEK3AIBmeD3T5T7/uokLLwMwWUVaFoYQNRVhnZh6MLMGa0+6ssY7qE3KhAOObCUBNzN3XMj6mNBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:34.288783Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.0402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ba812cdaf75e4ccbd12828eae78af0e5293ca0d89d1cfae01f577144b14e85d","sha256:be4c061af9eabccff07de09e8ac9e6ac0b3da0b2d4462c4f47a516307159a882"],"state_sha256":"d2c6514dc81bfacf82b2d5e0e845827a601532ab99b2eca1564c4161648fa1fa"}