{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TUP6BK4N67SBQNQ5WTAI7ALYTL","short_pith_number":"pith:TUP6BK4N","schema_version":"1.0","canonical_sha256":"9d1fe0ab8df7e418361db4c08f81789ac7329640d83bb928f49d348eb6b433c1","source":{"kind":"arxiv","id":"1110.2058","version":2},"attestation_state":"computed","paper":{"title":"Convergence Rates for Mixture-of-Experts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Eduardo F. Mendes, Wenxin Jiang","submitted_at":"2011-10-10T14:43:02Z","abstract_excerpt":"In mixtures-of-experts (ME) model, where a number of submodels (experts) are combined, there have been two longstanding problems: (i) how many experts should be chosen, given the size of the training data? (ii) given the total number of parameters, is it better to use a few very complex experts, or is it better to combine many simple experts? In this paper, we try to provide some insights to these problems through a theoretic study on a ME structure where $m$ experts are mixed, with each expert being related to a polynomial regression model of order $k$. We study the convergence rate of the ma"},"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":"1110.2058","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-10T14:43:02Z","cross_cats_sorted":["stat.ME","stat.ML","stat.TH"],"title_canon_sha256":"bedefaeb72e0172bb964b2b8f5f1445fa17d6249c542393f07120ce30e37cc1f","abstract_canon_sha256":"6094cc782b3aaf3f2c64c99df605af43f7f0903cf38c90b65f7c957f98d72aa7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:46.669903Z","signature_b64":"53jKNJluLJFfnqHn63UxiL0kgHvPISsqCmEyITEf6cqQ2yH0dhzwwdk7x5BJqbGagflChhX6YU/YxhVfn/ogDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d1fe0ab8df7e418361db4c08f81789ac7329640d83bb928f49d348eb6b433c1","last_reissued_at":"2026-05-18T04:09:46.669471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:46.669471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence Rates for Mixture-of-Experts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Eduardo F. Mendes, Wenxin Jiang","submitted_at":"2011-10-10T14:43:02Z","abstract_excerpt":"In mixtures-of-experts (ME) model, where a number of submodels (experts) are combined, there have been two longstanding problems: (i) how many experts should be chosen, given the size of the training data? (ii) given the total number of parameters, is it better to use a few very complex experts, or is it better to combine many simple experts? In this paper, we try to provide some insights to these problems through a theoretic study on a ME structure where $m$ experts are mixed, with each expert being related to a polynomial regression model of order $k$. We study the convergence rate of the ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2058","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":"1110.2058","created_at":"2026-05-18T04:09:46.669537+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.2058v2","created_at":"2026-05-18T04:09:46.669537+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2058","created_at":"2026-05-18T04:09:46.669537+00:00"},{"alias_kind":"pith_short_12","alias_value":"TUP6BK4N67SB","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TUP6BK4N67SBQNQ5","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TUP6BK4N","created_at":"2026-05-18T12:26:42.757692+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.25852","citing_title":"A Post-Processing Conformal Prediction Approach for Conditional Coverage via Pivotal Scores","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TUP6BK4N67SBQNQ5WTAI7ALYTL","json":"https://pith.science/pith/TUP6BK4N67SBQNQ5WTAI7ALYTL.json","graph_json":"https://pith.science/api/pith-number/TUP6BK4N67SBQNQ5WTAI7ALYTL/graph.json","events_json":"https://pith.science/api/pith-number/TUP6BK4N67SBQNQ5WTAI7ALYTL/events.json","paper":"https://pith.science/paper/TUP6BK4N"},"agent_actions":{"view_html":"https://pith.science/pith/TUP6BK4N67SBQNQ5WTAI7ALYTL","download_json":"https://pith.science/pith/TUP6BK4N67SBQNQ5WTAI7ALYTL.json","view_paper":"https://pith.science/paper/TUP6BK4N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.2058&json=true","fetch_graph":"https://pith.science/api/pith-number/TUP6BK4N67SBQNQ5WTAI7ALYTL/graph.json","fetch_events":"https://pith.science/api/pith-number/TUP6BK4N67SBQNQ5WTAI7ALYTL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TUP6BK4N67SBQNQ5WTAI7ALYTL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TUP6BK4N67SBQNQ5WTAI7ALYTL/action/storage_attestation","attest_author":"https://pith.science/pith/TUP6BK4N67SBQNQ5WTAI7ALYTL/action/author_attestation","sign_citation":"https://pith.science/pith/TUP6BK4N67SBQNQ5WTAI7ALYTL/action/citation_signature","submit_replication":"https://pith.science/pith/TUP6BK4N67SBQNQ5WTAI7ALYTL/action/replication_record"}},"created_at":"2026-05-18T04:09:46.669537+00:00","updated_at":"2026-05-18T04:09:46.669537+00:00"}