{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:6MPNXLSEVYEWTOIRGYD5ZU6M5E","short_pith_number":"pith:6MPNXLSE","schema_version":"1.0","canonical_sha256":"f31edbae44ae0969b9113607dcd3cce93342cf49319098ec44049578f495a779","source":{"kind":"arxiv","id":"1209.4280","version":1},"attestation_state":"computed","paper":{"title":"Alpha/Beta Divergences and Tweedie Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"A. Taylan Cemgil, Y. Kenan Yilmaz","submitted_at":"2012-09-19T15:20:47Z","abstract_excerpt":"We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential dispersion models. Starting from the variance function of a Tweedie model, we outline how to get alpha and beta divergences as special cases of Csisz\\'ar's $f$ and Bregman divergences. This result directly generalizes the well-known relationship between the Gaussian distribution and least squares estimation to Tweedie models and beta divergence minimization."},"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":"1209.4280","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2012-09-19T15:20:47Z","cross_cats_sorted":["cs.IT","math.IT","math.ST","stat.TH"],"title_canon_sha256":"97cef46d39db39e2732158fe5f01894e5c8e784415c59994d16e7cf12fb9f566","abstract_canon_sha256":"60f22923716ec231deeb9bd55d20a7b84412770344c97a2f86aee80bb66b3950"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:13.030246Z","signature_b64":"lMY9fp9V/WKdRC+OpVwjCayjbgkFpq9VWqF/tFf3cHpoHhaqiLMOsp1XIGbQPdMlGlv0+ra9beCwIAaMfEWGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f31edbae44ae0969b9113607dcd3cce93342cf49319098ec44049578f495a779","last_reissued_at":"2026-05-18T03:45:13.029471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:13.029471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Alpha/Beta Divergences and Tweedie Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"A. Taylan Cemgil, Y. Kenan Yilmaz","submitted_at":"2012-09-19T15:20:47Z","abstract_excerpt":"We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential dispersion models. Starting from the variance function of a Tweedie model, we outline how to get alpha and beta divergences as special cases of Csisz\\'ar's $f$ and Bregman divergences. This result directly generalizes the well-known relationship between the Gaussian distribution and least squares estimation to Tweedie models and beta divergence minimization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4280","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1209.4280","created_at":"2026-05-18T03:45:13.029582+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.4280v1","created_at":"2026-05-18T03:45:13.029582+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4280","created_at":"2026-05-18T03:45:13.029582+00:00"},{"alias_kind":"pith_short_12","alias_value":"6MPNXLSEVYEW","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6MPNXLSEVYEWTOIR","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6MPNXLSE","created_at":"2026-05-18T12:26:56.085431+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6MPNXLSEVYEWTOIRGYD5ZU6M5E","json":"https://pith.science/pith/6MPNXLSEVYEWTOIRGYD5ZU6M5E.json","graph_json":"https://pith.science/api/pith-number/6MPNXLSEVYEWTOIRGYD5ZU6M5E/graph.json","events_json":"https://pith.science/api/pith-number/6MPNXLSEVYEWTOIRGYD5ZU6M5E/events.json","paper":"https://pith.science/paper/6MPNXLSE"},"agent_actions":{"view_html":"https://pith.science/pith/6MPNXLSEVYEWTOIRGYD5ZU6M5E","download_json":"https://pith.science/pith/6MPNXLSEVYEWTOIRGYD5ZU6M5E.json","view_paper":"https://pith.science/paper/6MPNXLSE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.4280&json=true","fetch_graph":"https://pith.science/api/pith-number/6MPNXLSEVYEWTOIRGYD5ZU6M5E/graph.json","fetch_events":"https://pith.science/api/pith-number/6MPNXLSEVYEWTOIRGYD5ZU6M5E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6MPNXLSEVYEWTOIRGYD5ZU6M5E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6MPNXLSEVYEWTOIRGYD5ZU6M5E/action/storage_attestation","attest_author":"https://pith.science/pith/6MPNXLSEVYEWTOIRGYD5ZU6M5E/action/author_attestation","sign_citation":"https://pith.science/pith/6MPNXLSEVYEWTOIRGYD5ZU6M5E/action/citation_signature","submit_replication":"https://pith.science/pith/6MPNXLSEVYEWTOIRGYD5ZU6M5E/action/replication_record"}},"created_at":"2026-05-18T03:45:13.029582+00:00","updated_at":"2026-05-18T03:45:13.029582+00:00"}