{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ION333QMGV4QAXW75TN4YEDK7O","short_pith_number":"pith:ION333QM","schema_version":"1.0","canonical_sha256":"439bbdee0c3579005edfecdbcc106afbb15d5d9311eb93f84ba6e6ad4e0d1ada","source":{"kind":"arxiv","id":"2506.07504","version":1},"attestation_state":"computed","paper":{"title":"Minimax Optimal Rates for Regression on Manifolds and Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Rong Tang, Yun Yang","submitted_at":"2025-06-09T07:28:00Z","abstract_excerpt":"Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods. Classical nonparametric techniques often assume that the conditional distribution has a well-defined density, an assumption that fails in many real-world settings. These include cases where data contain discrete elements or lie on complex low-dimensional structures within high-dimensional spaces. In this work, we establish minimax convergence rates for distribution"},"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":"2506.07504","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-06-09T07:28:00Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a04caa30ed2204fb43699dba37c89d8a38f8fbef483650d126c46888ba870df0","abstract_canon_sha256":"4ce843c56454fa3d223ecb065b254f933f9c8c8fb859b0b4fc8568f616692606"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:28.444687Z","signature_b64":"uER5hs5K6q3wT4zS000nqxWEg/6VmPgYtObEqzNCRU2+eXVsrxINMiK7RpV5TTY1vQON6ArkI6aJQ74bVmQYCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"439bbdee0c3579005edfecdbcc106afbb15d5d9311eb93f84ba6e6ad4e0d1ada","last_reissued_at":"2026-07-05T11:18:28.444140Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:28.444140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimax Optimal Rates for Regression on Manifolds and Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Rong Tang, Yun Yang","submitted_at":"2025-06-09T07:28:00Z","abstract_excerpt":"Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods. Classical nonparametric techniques often assume that the conditional distribution has a well-defined density, an assumption that fails in many real-world settings. These include cases where data contain discrete elements or lie on complex low-dimensional structures within high-dimensional spaces. In this work, we establish minimax convergence rates for distribution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07504","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.07504/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":"2506.07504","created_at":"2026-07-05T11:18:28.444195+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.07504v1","created_at":"2026-07-05T11:18:28.444195+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07504","created_at":"2026-07-05T11:18:28.444195+00:00"},{"alias_kind":"pith_short_12","alias_value":"ION333QMGV4Q","created_at":"2026-07-05T11:18:28.444195+00:00"},{"alias_kind":"pith_short_16","alias_value":"ION333QMGV4QAXW7","created_at":"2026-07-05T11:18:28.444195+00:00"},{"alias_kind":"pith_short_8","alias_value":"ION333QM","created_at":"2026-07-05T11:18:28.444195+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/ION333QMGV4QAXW75TN4YEDK7O","json":"https://pith.science/pith/ION333QMGV4QAXW75TN4YEDK7O.json","graph_json":"https://pith.science/api/pith-number/ION333QMGV4QAXW75TN4YEDK7O/graph.json","events_json":"https://pith.science/api/pith-number/ION333QMGV4QAXW75TN4YEDK7O/events.json","paper":"https://pith.science/paper/ION333QM"},"agent_actions":{"view_html":"https://pith.science/pith/ION333QMGV4QAXW75TN4YEDK7O","download_json":"https://pith.science/pith/ION333QMGV4QAXW75TN4YEDK7O.json","view_paper":"https://pith.science/paper/ION333QM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.07504&json=true","fetch_graph":"https://pith.science/api/pith-number/ION333QMGV4QAXW75TN4YEDK7O/graph.json","fetch_events":"https://pith.science/api/pith-number/ION333QMGV4QAXW75TN4YEDK7O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ION333QMGV4QAXW75TN4YEDK7O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ION333QMGV4QAXW75TN4YEDK7O/action/storage_attestation","attest_author":"https://pith.science/pith/ION333QMGV4QAXW75TN4YEDK7O/action/author_attestation","sign_citation":"https://pith.science/pith/ION333QMGV4QAXW75TN4YEDK7O/action/citation_signature","submit_replication":"https://pith.science/pith/ION333QMGV4QAXW75TN4YEDK7O/action/replication_record"}},"created_at":"2026-07-05T11:18:28.444195+00:00","updated_at":"2026-07-05T11:18:28.444195+00:00"}