{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:EM4RAR4RVAU7UAGL447U7NA2H5","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":"5e1b66a573ef36aea13cf0ec77f4d23078e04a48081125ca073cd5930c6d4461","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-02-14T18:42:11Z","title_canon_sha256":"a7040df3f7f8eee4d1c2d196e10789fb24e1dfe5ce012959a9e7860653a83931"},"schema_version":"1.0","source":{"id":"2202.06930","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.06930","created_at":"2026-07-05T04:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"2202.06930v2","created_at":"2026-07-05T04:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.06930","created_at":"2026-07-05T04:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"EM4RAR4RVAU7","created_at":"2026-07-05T04:07:07Z"},{"alias_kind":"pith_short_16","alias_value":"EM4RAR4RVAU7UAGL","created_at":"2026-07-05T04:07:07Z"},{"alias_kind":"pith_short_8","alias_value":"EM4RAR4R","created_at":"2026-07-05T04:07:07Z"}],"graph_snapshots":[{"event_id":"sha256:661ee700b49929e49655b548a74ad459744dccdd7f9dc1440849a8d24dfd9db7","target":"graph","created_at":"2026-07-05T04:07:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2202.06930/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The $d$-th moment of an $n$-dimensional random variable is a symmetric $d$-way tensor of size $n^d$, so working with moments naively is assumed to be prohibitively expensive for $d>2$ and larger values of $n$. In this work, we develop theory and numerical methods for \\emph{implicit computations} with moment tensors of GMMs, reducing the computational and storage costs to $\\mathcal{O}(n^2)$ and $\\mathcal{O}(n^3)$, respectively, for general covariance ma","authors_text":"Jo\\~ao M. Pereira, Joe Kileel, Tamara G. Kolda","cross_cats":["cs.LG","cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-02-14T18:42:11Z","title":"Tensor Moments of Gaussian Mixture Models: Theory and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.06930","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":"sha256:7affb70bb32813779fd54f2573f3ff923fb441bcc002bfada31badead9563619","target":"record","created_at":"2026-07-05T04:07:07Z","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":"5e1b66a573ef36aea13cf0ec77f4d23078e04a48081125ca073cd5930c6d4461","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-02-14T18:42:11Z","title_canon_sha256":"a7040df3f7f8eee4d1c2d196e10789fb24e1dfe5ce012959a9e7860653a83931"},"schema_version":"1.0","source":{"id":"2202.06930","kind":"arxiv","version":2}},"canonical_sha256":"2339104791a829fa00cbe73f4fb41a3f450f2ba98809983763b024bca876a115","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2339104791a829fa00cbe73f4fb41a3f450f2ba98809983763b024bca876a115","first_computed_at":"2026-07-05T04:07:07.650796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:07:07.650796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Euu2ycNJMc5OeBKxpdiEyE8uzdEaIe9MwGjuq3g5Z+L5QK1KtssG689nWOSdc6t0XU/m6VE00ymS0woBl4TCA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:07:07.651335Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.06930","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7affb70bb32813779fd54f2573f3ff923fb441bcc002bfada31badead9563619","sha256:661ee700b49929e49655b548a74ad459744dccdd7f9dc1440849a8d24dfd9db7"],"state_sha256":"ab4016076f808c1246cf5199d2a33b3a2f8c1350ac25b655bfc35e04ed5fbe8c"}