{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PERLJ5CE5LYAD47ZRRHUJVCAMV","short_pith_number":"pith:PERLJ5CE","schema_version":"1.0","canonical_sha256":"7922b4f444eaf001f3f98c4f44d4406572c2e24eff798dde076d0adb5cbf42c7","source":{"kind":"arxiv","id":"1312.3516","version":4},"attestation_state":"computed","paper":{"title":"Density Estimation in Infinite Dimensional Exponential Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Aapo Hyv\\\"arinen, Arthur Gretton, Bharath Sriperumbudur, Kenji Fukumizu, Revant Kumar","submitted_at":"2013-12-12T15:09:25Z","abstract_excerpt":"In this paper, we consider an infinite dimensional exponential family, $\\mathcal{P}$ of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space, $H$ and show it to be quite rich in the sense that a broad class of densities on $\\mathbb{R}^d$ can be approximated arbitrarily well in Kullback-Leibler (KL) divergence by elements in $\\mathcal{P}$. The main goal of the paper is to estimate an unknown density, $p_0$ through an element in $\\mathcal{P}$. Standard techniques like maximum likelihood estimation (MLE) or pseudo MLE (based on the method of sieves), wh"},"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":"1312.3516","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-12-12T15:09:25Z","cross_cats_sorted":["stat.ME","stat.ML","stat.TH"],"title_canon_sha256":"76daab7e02631c24f2b2931d80ae374548d529592ffe44daf735eb3cba32cd3f","abstract_canon_sha256":"3d55abab535bb690be38e8276363602c69ea16225cd10b04b7616123f8b5b451"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:39.977709Z","signature_b64":"xlI20835NST7zsWJ2zWh7VBIQKHh9j+Dr0yQJYEyOihdj95YCwGSNf1Rpu+0hFbDatJMJ248Exp7bnEaYUnmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7922b4f444eaf001f3f98c4f44d4406572c2e24eff798dde076d0adb5cbf42c7","last_reissued_at":"2026-05-18T00:43:39.977083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:39.977083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Density Estimation in Infinite Dimensional Exponential Families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Aapo Hyv\\\"arinen, Arthur Gretton, Bharath Sriperumbudur, Kenji Fukumizu, Revant Kumar","submitted_at":"2013-12-12T15:09:25Z","abstract_excerpt":"In this paper, we consider an infinite dimensional exponential family, $\\mathcal{P}$ of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space, $H$ and show it to be quite rich in the sense that a broad class of densities on $\\mathbb{R}^d$ can be approximated arbitrarily well in Kullback-Leibler (KL) divergence by elements in $\\mathcal{P}$. The main goal of the paper is to estimate an unknown density, $p_0$ through an element in $\\mathcal{P}$. Standard techniques like maximum likelihood estimation (MLE) or pseudo MLE (based on the method of sieves), wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3516","kind":"arxiv","version":4},"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":"1312.3516","created_at":"2026-05-18T00:43:39.977173+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.3516v4","created_at":"2026-05-18T00:43:39.977173+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3516","created_at":"2026-05-18T00:43:39.977173+00:00"},{"alias_kind":"pith_short_12","alias_value":"PERLJ5CE5LYA","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PERLJ5CE5LYAD47Z","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PERLJ5CE","created_at":"2026-05-18T12:27:54.935989+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.03240","citing_title":"On Model-Based Clustering With Entropic Optimal Transport","ref_index":131,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PERLJ5CE5LYAD47ZRRHUJVCAMV","json":"https://pith.science/pith/PERLJ5CE5LYAD47ZRRHUJVCAMV.json","graph_json":"https://pith.science/api/pith-number/PERLJ5CE5LYAD47ZRRHUJVCAMV/graph.json","events_json":"https://pith.science/api/pith-number/PERLJ5CE5LYAD47ZRRHUJVCAMV/events.json","paper":"https://pith.science/paper/PERLJ5CE"},"agent_actions":{"view_html":"https://pith.science/pith/PERLJ5CE5LYAD47ZRRHUJVCAMV","download_json":"https://pith.science/pith/PERLJ5CE5LYAD47ZRRHUJVCAMV.json","view_paper":"https://pith.science/paper/PERLJ5CE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.3516&json=true","fetch_graph":"https://pith.science/api/pith-number/PERLJ5CE5LYAD47ZRRHUJVCAMV/graph.json","fetch_events":"https://pith.science/api/pith-number/PERLJ5CE5LYAD47ZRRHUJVCAMV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PERLJ5CE5LYAD47ZRRHUJVCAMV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PERLJ5CE5LYAD47ZRRHUJVCAMV/action/storage_attestation","attest_author":"https://pith.science/pith/PERLJ5CE5LYAD47ZRRHUJVCAMV/action/author_attestation","sign_citation":"https://pith.science/pith/PERLJ5CE5LYAD47ZRRHUJVCAMV/action/citation_signature","submit_replication":"https://pith.science/pith/PERLJ5CE5LYAD47ZRRHUJVCAMV/action/replication_record"}},"created_at":"2026-05-18T00:43:39.977173+00:00","updated_at":"2026-05-18T00:43:39.977173+00:00"}