{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NMWODHFA2FGAMYIGV6FJIM5TJD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0f96e0c608b7c9c76fac0ae2b18326a6eb7639010de4eaf14aa43307e525c08c","cross_cats_sorted":["cs.LG","math.FA","math.OC","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-21T12:36:39Z","title_canon_sha256":"59ccb4b51b41048cd37c39ad7840c17b4d1ae1424cba1722ea2711d554e68601"},"schema_version":"1.0","source":{"id":"1710.07797","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.07797","created_at":"2026-05-18T00:32:19Z"},{"alias_kind":"arxiv_version","alias_value":"1710.07797v1","created_at":"2026-05-18T00:32:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07797","created_at":"2026-05-18T00:32:19Z"},{"alias_kind":"pith_short_12","alias_value":"NMWODHFA2FGA","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NMWODHFA2FGAMYIG","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NMWODHFA","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:dc8714d9d60453a09d8fc9afb3a2ef60bb127fb28a99caa70c591ce9c6e05ed5","target":"graph","created_at":"2026-05-18T00:32:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nystr\\\"om subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied algorithm are provided. Particularly, optimal learning rates are derived considering different possible choices of the step-size, the mini-batch size, the number of iterations/passes, and the subsampling level. In comparison with state-of-the-art algorithms such as the classic stochastic gradient methods and kernel ridge regression with Nystr\\\"om, the studied","authors_text":"Junhong Lin, Lorenzo Rosasco","cross_cats":["cs.LG","math.FA","math.OC","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-21T12:36:39Z","title":"Optimal Rates for Learning with Nystr\\\"om Stochastic Gradient Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07797","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1bbe143c090533e6778e4ef661c94cf2cd82bca8f90302a2825c116df87d90e8","target":"record","created_at":"2026-05-18T00:32:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0f96e0c608b7c9c76fac0ae2b18326a6eb7639010de4eaf14aa43307e525c08c","cross_cats_sorted":["cs.LG","math.FA","math.OC","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-10-21T12:36:39Z","title_canon_sha256":"59ccb4b51b41048cd37c39ad7840c17b4d1ae1424cba1722ea2711d554e68601"},"schema_version":"1.0","source":{"id":"1710.07797","kind":"arxiv","version":1}},"canonical_sha256":"6b2ce19ca0d14c066106af8a9433b348d487c1cf96b5dc57192ee2ab6ef0eea4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b2ce19ca0d14c066106af8a9433b348d487c1cf96b5dc57192ee2ab6ef0eea4","first_computed_at":"2026-05-18T00:32:19.650998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:19.650998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1moGxoFyzhZRS3b27sFyDsAmT3XFveA6wOoPaPlFVdbluIg5Oz+Ty7HCTn29xSFmERJzBiIUiHt9Mv5WqJ0bDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:19.651659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.07797","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bbe143c090533e6778e4ef661c94cf2cd82bca8f90302a2825c116df87d90e8","sha256:dc8714d9d60453a09d8fc9afb3a2ef60bb127fb28a99caa70c591ce9c6e05ed5"],"state_sha256":"ef16e2fc2ce0a63454a46840e1a22b78237577cd01988315b57752b953cb340f"}