{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:VCULRPADFIV2D6RPSRAVVB2KLR","short_pith_number":"pith:VCULRPAD","schema_version":"1.0","canonical_sha256":"a8a8b8bc032a2ba1fa2f94415a874a5c55b8f83219f9124579e3791a867f9aa3","source":{"kind":"arxiv","id":"1306.0407","version":2},"attestation_state":"computed","paper":{"title":"Constructive Setting of the Density Ratio Estimation Problem and its Rigorous Solution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Igor Braga, Rauf Izmailov, Vladimir Vapnik","submitted_at":"2013-06-03T13:54:34Z","abstract_excerpt":"We introduce a general constructive setting of the density ratio estimation problem as a solution of a (multidimensional) integral equation. In this equation, not only its right hand side is known approximately, but also the integral operator is defined approximately. We show that this ill-posed problem has a rigorous solution and obtain the solution in a closed form. The key element of this solution is the novel V-matrix, which captures the geometry of the observed samples. We compare our method with three well-known previously proposed ones. Our experimental results demonstrate the good pote"},"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":"1306.0407","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2013-06-03T13:54:34Z","cross_cats_sorted":[],"title_canon_sha256":"e02b9935604fbbf28686448b8112a4272737fd93cff99a8d379133e3c84322bb","abstract_canon_sha256":"c3dcb793ea65990b965d56d8c766cc6d7a49362a492c8b96e2cb2a4ca6aae806"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:47.457332Z","signature_b64":"UN3czjfwi342DGC+5LCQgrTJ5/6qKgdPZbdAxn51LPlhjgPn+uY+vXCtOQmyleuKa+AXqhgsD+ijSfcX9bq2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8a8b8bc032a2ba1fa2f94415a874a5c55b8f83219f9124579e3791a867f9aa3","last_reissued_at":"2026-05-18T03:20:47.456531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:47.456531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructive Setting of the Density Ratio Estimation Problem and its Rigorous Solution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Igor Braga, Rauf Izmailov, Vladimir Vapnik","submitted_at":"2013-06-03T13:54:34Z","abstract_excerpt":"We introduce a general constructive setting of the density ratio estimation problem as a solution of a (multidimensional) integral equation. In this equation, not only its right hand side is known approximately, but also the integral operator is defined approximately. We show that this ill-posed problem has a rigorous solution and obtain the solution in a closed form. The key element of this solution is the novel V-matrix, which captures the geometry of the observed samples. We compare our method with three well-known previously proposed ones. Our experimental results demonstrate the good pote"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0407","kind":"arxiv","version":2},"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":"1306.0407","created_at":"2026-05-18T03:20:47.456653+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.0407v2","created_at":"2026-05-18T03:20:47.456653+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0407","created_at":"2026-05-18T03:20:47.456653+00:00"},{"alias_kind":"pith_short_12","alias_value":"VCULRPADFIV2","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VCULRPADFIV2D6RP","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VCULRPAD","created_at":"2026-05-18T12:28:04.890932+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/VCULRPADFIV2D6RPSRAVVB2KLR","json":"https://pith.science/pith/VCULRPADFIV2D6RPSRAVVB2KLR.json","graph_json":"https://pith.science/api/pith-number/VCULRPADFIV2D6RPSRAVVB2KLR/graph.json","events_json":"https://pith.science/api/pith-number/VCULRPADFIV2D6RPSRAVVB2KLR/events.json","paper":"https://pith.science/paper/VCULRPAD"},"agent_actions":{"view_html":"https://pith.science/pith/VCULRPADFIV2D6RPSRAVVB2KLR","download_json":"https://pith.science/pith/VCULRPADFIV2D6RPSRAVVB2KLR.json","view_paper":"https://pith.science/paper/VCULRPAD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.0407&json=true","fetch_graph":"https://pith.science/api/pith-number/VCULRPADFIV2D6RPSRAVVB2KLR/graph.json","fetch_events":"https://pith.science/api/pith-number/VCULRPADFIV2D6RPSRAVVB2KLR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VCULRPADFIV2D6RPSRAVVB2KLR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VCULRPADFIV2D6RPSRAVVB2KLR/action/storage_attestation","attest_author":"https://pith.science/pith/VCULRPADFIV2D6RPSRAVVB2KLR/action/author_attestation","sign_citation":"https://pith.science/pith/VCULRPADFIV2D6RPSRAVVB2KLR/action/citation_signature","submit_replication":"https://pith.science/pith/VCULRPADFIV2D6RPSRAVVB2KLR/action/replication_record"}},"created_at":"2026-05-18T03:20:47.456653+00:00","updated_at":"2026-05-18T03:20:47.456653+00:00"}