{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:AY4UEG2N365OUT6YWENWCZI3SA","short_pith_number":"pith:AY4UEG2N","schema_version":"1.0","canonical_sha256":"0639421b4ddfbaea4fd8b11b61651b900b9ed2c3c9b351e0fb58f33e40ffb299","source":{"kind":"arxiv","id":"1010.0072","version":2},"attestation_state":"computed","paper":{"title":"Linear regression through PAC-Bayesian truncation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"INRIA Paris - Rocquencourt), Jean-Yves Audibert (INRIA Paris - Rocquencourt), Olivier Catoni (DMA","submitted_at":"2010-10-01T06:20:15Z","abstract_excerpt":"We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression under L^\\infty constraints on the linear combination. When the input distribution is known, there already exists an algorithm having an expected excess risk of order d/n, where n is the size of the training data. Without this strong assumption, standard results often contain a multiplicative log(n) factor, complex constants involving the conditioning of the Gram matrix of the covariates, kurtosis coefficients or some geometric quantity characterizing the relation betwee"},"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":"1010.0072","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-10-01T06:20:15Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e19b0f3a06179b4db99eecafc3097f37aded4fc8fc3d5d264009d351ed1bb80d","abstract_canon_sha256":"3d7cc6b43d129b1c55a7381f7b3ab0436ab5d62bbd79e0f9b3a3d8bfebee77d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:16.077435Z","signature_b64":"zg5hz5h5fxu1kb6xCO2g+ivWMHQ34TGS4zkAAV72gWyf8Ddv37x8ep6GjMWsnELxn+g0eEiNdj6kIl54AEAlBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0639421b4ddfbaea4fd8b11b61651b900b9ed2c3c9b351e0fb58f33e40ffb299","last_reissued_at":"2026-05-18T04:13:16.076897Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:16.076897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear regression through PAC-Bayesian truncation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"INRIA Paris - Rocquencourt), Jean-Yves Audibert (INRIA Paris - Rocquencourt), Olivier Catoni (DMA","submitted_at":"2010-10-01T06:20:15Z","abstract_excerpt":"We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression under L^\\infty constraints on the linear combination. When the input distribution is known, there already exists an algorithm having an expected excess risk of order d/n, where n is the size of the training data. Without this strong assumption, standard results often contain a multiplicative log(n) factor, complex constants involving the conditioning of the Gram matrix of the covariates, kurtosis coefficients or some geometric quantity characterizing the relation betwee"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0072","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":"1010.0072","created_at":"2026-05-18T04:13:16.076970+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.0072v2","created_at":"2026-05-18T04:13:16.076970+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0072","created_at":"2026-05-18T04:13:16.076970+00:00"},{"alias_kind":"pith_short_12","alias_value":"AY4UEG2N365O","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"AY4UEG2N365OUT6Y","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"AY4UEG2N","created_at":"2026-05-18T12:26:05.355336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.03674","citing_title":"Statistical Inference via T-Posterior Randomised Estimators","ref_index":3,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AY4UEG2N365OUT6YWENWCZI3SA","json":"https://pith.science/pith/AY4UEG2N365OUT6YWENWCZI3SA.json","graph_json":"https://pith.science/api/pith-number/AY4UEG2N365OUT6YWENWCZI3SA/graph.json","events_json":"https://pith.science/api/pith-number/AY4UEG2N365OUT6YWENWCZI3SA/events.json","paper":"https://pith.science/paper/AY4UEG2N"},"agent_actions":{"view_html":"https://pith.science/pith/AY4UEG2N365OUT6YWENWCZI3SA","download_json":"https://pith.science/pith/AY4UEG2N365OUT6YWENWCZI3SA.json","view_paper":"https://pith.science/paper/AY4UEG2N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.0072&json=true","fetch_graph":"https://pith.science/api/pith-number/AY4UEG2N365OUT6YWENWCZI3SA/graph.json","fetch_events":"https://pith.science/api/pith-number/AY4UEG2N365OUT6YWENWCZI3SA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AY4UEG2N365OUT6YWENWCZI3SA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AY4UEG2N365OUT6YWENWCZI3SA/action/storage_attestation","attest_author":"https://pith.science/pith/AY4UEG2N365OUT6YWENWCZI3SA/action/author_attestation","sign_citation":"https://pith.science/pith/AY4UEG2N365OUT6YWENWCZI3SA/action/citation_signature","submit_replication":"https://pith.science/pith/AY4UEG2N365OUT6YWENWCZI3SA/action/replication_record"}},"created_at":"2026-05-18T04:13:16.076970+00:00","updated_at":"2026-05-18T04:13:16.076970+00:00"}