{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:T7IYOUITGGYXLHITFIANJSIR6Q","short_pith_number":"pith:T7IYOUIT","schema_version":"1.0","canonical_sha256":"9fd187511331b1759d132a00d4c911f411d99b62b31b4bcc05724d9c59195108","source":{"kind":"arxiv","id":"1708.00568","version":3},"attestation_state":"computed","paper":{"title":"On $w$-mixtures: Finite convex combinations of prescribed component distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Frank Nielsen, Richard Nock","submitted_at":"2017-08-02T01:05:19Z","abstract_excerpt":"We consider the space of $w$-mixtures which is defined as the set of finite statistical mixtures sharing the same prescribed component distributions closed under convex combinations. The information geometry induced by the Bregman generator set to the Shannon negentropy on this space yields a dually flat space called the mixture family manifold. We show how the Kullback-Leibler (KL) divergence can be recovered from the corresponding Bregman divergence for the negentropy generator: That is, the KL divergence between two $w$-mixtures amounts to a Bregman Divergence (BD) induced by the Shannon ne"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1708.00568","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-08-02T01:05:19Z","cross_cats_sorted":[],"title_canon_sha256":"49d3da215f6be96cc5dde5a3ee8ca1c02551d2fa7c4d2ada27fa9a8280efdcea","abstract_canon_sha256":"8b0d52b5e12083787c2ccbbc9de5cc3ce554ccaf6b6e020fdabeb8704411afd6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:46:56.740138Z","signature_b64":"9c8EIcCtwM00XuWxWHCTBNU4rWFnruVZI9aLT12v2gaw3E9z2tSJKeJKxHEjRBmArfHPFZFh3sUYaEWhqa9MCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fd187511331b1759d132a00d4c911f411d99b62b31b4bcc05724d9c59195108","last_reissued_at":"2026-07-05T02:46:56.739695Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:46:56.739695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $w$-mixtures: Finite convex combinations of prescribed component distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Frank Nielsen, Richard Nock","submitted_at":"2017-08-02T01:05:19Z","abstract_excerpt":"We consider the space of $w$-mixtures which is defined as the set of finite statistical mixtures sharing the same prescribed component distributions closed under convex combinations. The information geometry induced by the Bregman generator set to the Shannon negentropy on this space yields a dually flat space called the mixture family manifold. We show how the Kullback-Leibler (KL) divergence can be recovered from the corresponding Bregman divergence for the negentropy generator: That is, the KL divergence between two $w$-mixtures amounts to a Bregman Divergence (BD) induced by the Shannon ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00568","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1708.00568/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1708.00568","created_at":"2026-07-05T02:46:56.739751+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.00568v3","created_at":"2026-07-05T02:46:56.739751+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00568","created_at":"2026-07-05T02:46:56.739751+00:00"},{"alias_kind":"pith_short_12","alias_value":"T7IYOUITGGYX","created_at":"2026-07-05T02:46:56.739751+00:00"},{"alias_kind":"pith_short_16","alias_value":"T7IYOUITGGYXLHIT","created_at":"2026-07-05T02:46:56.739751+00:00"},{"alias_kind":"pith_short_8","alias_value":"T7IYOUIT","created_at":"2026-07-05T02:46:56.739751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.21396","citing_title":"PMODE: Theoretically Grounded and Modular Mixture Modeling","ref_index":46,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T7IYOUITGGYXLHITFIANJSIR6Q","json":"https://pith.science/pith/T7IYOUITGGYXLHITFIANJSIR6Q.json","graph_json":"https://pith.science/api/pith-number/T7IYOUITGGYXLHITFIANJSIR6Q/graph.json","events_json":"https://pith.science/api/pith-number/T7IYOUITGGYXLHITFIANJSIR6Q/events.json","paper":"https://pith.science/paper/T7IYOUIT"},"agent_actions":{"view_html":"https://pith.science/pith/T7IYOUITGGYXLHITFIANJSIR6Q","download_json":"https://pith.science/pith/T7IYOUITGGYXLHITFIANJSIR6Q.json","view_paper":"https://pith.science/paper/T7IYOUIT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.00568&json=true","fetch_graph":"https://pith.science/api/pith-number/T7IYOUITGGYXLHITFIANJSIR6Q/graph.json","fetch_events":"https://pith.science/api/pith-number/T7IYOUITGGYXLHITFIANJSIR6Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T7IYOUITGGYXLHITFIANJSIR6Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T7IYOUITGGYXLHITFIANJSIR6Q/action/storage_attestation","attest_author":"https://pith.science/pith/T7IYOUITGGYXLHITFIANJSIR6Q/action/author_attestation","sign_citation":"https://pith.science/pith/T7IYOUITGGYXLHITFIANJSIR6Q/action/citation_signature","submit_replication":"https://pith.science/pith/T7IYOUITGGYXLHITFIANJSIR6Q/action/replication_record"}},"created_at":"2026-07-05T02:46:56.739751+00:00","updated_at":"2026-07-05T02:46:56.739751+00:00"}