{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:VCZTB5VE5UECJE3XTPAHAKDMNY","short_pith_number":"pith:VCZTB5VE","canonical_record":{"source":{"id":"2103.05238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-03-09T05:57:08Z","cross_cats_sorted":["cs.LG","stat.CO"],"title_canon_sha256":"fba76dd21a12260b252b49cbc35feadb3452f3100484e014529eb07a4f8616af","abstract_canon_sha256":"3ab2802366b3a8a7fe1647f9310e263dd7cb0007d03db756991074b0d5ea6374"},"schema_version":"1.0"},"canonical_sha256":"a8b330f6a4ed082493779bc070286c6e1e813ee9070732e90b063379c7537e32","source":{"kind":"arxiv","id":"2103.05238","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.05238","created_at":"2026-07-05T02:21:24Z"},{"alias_kind":"arxiv_version","alias_value":"2103.05238v1","created_at":"2026-07-05T02:21:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.05238","created_at":"2026-07-05T02:21:24Z"},{"alias_kind":"pith_short_12","alias_value":"VCZTB5VE5UEC","created_at":"2026-07-05T02:21:24Z"},{"alias_kind":"pith_short_16","alias_value":"VCZTB5VE5UECJE3X","created_at":"2026-07-05T02:21:24Z"},{"alias_kind":"pith_short_8","alias_value":"VCZTB5VE","created_at":"2026-07-05T02:21:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:VCZTB5VE5UECJE3XTPAHAKDMNY","target":"record","payload":{"canonical_record":{"source":{"id":"2103.05238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-03-09T05:57:08Z","cross_cats_sorted":["cs.LG","stat.CO"],"title_canon_sha256":"fba76dd21a12260b252b49cbc35feadb3452f3100484e014529eb07a4f8616af","abstract_canon_sha256":"3ab2802366b3a8a7fe1647f9310e263dd7cb0007d03db756991074b0d5ea6374"},"schema_version":"1.0"},"canonical_sha256":"a8b330f6a4ed082493779bc070286c6e1e813ee9070732e90b063379c7537e32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:21:24.071613Z","signature_b64":"mfyGTAb06Fjmyn0MM3utJnCwze2ELMELjPVWVS8nbIIp/nJurr27jqlZfcWChVtfqpiSkkTmH3IpM1CpgkvEAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8b330f6a4ed082493779bc070286c6e1e813ee9070732e90b063379c7537e32","last_reissued_at":"2026-07-05T02:21:24.071151Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:21:24.071151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2103.05238","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:21:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0yuoczrEkIB/S8DjtOj6JlGxC6rKeXRuPpCJEkQuZvCSeX4xE8iMDPk8deJMKrqLKx/rxXJVQdWtTWGX6sGxCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T20:12:35.347573Z"},"content_sha256":"3d48eb63834e4ed444419787a32c3c05e726af5ab800f127c78bb0dca19f8520","schema_version":"1.0","event_id":"sha256:3d48eb63834e4ed444419787a32c3c05e726af5ab800f127c78bb0dca19f8520"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:VCZTB5VE5UECJE3XTPAHAKDMNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast Statistical Leverage Score Approximation in Kernel Ridge Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.CO"],"primary_cat":"stat.ML","authors_text":"Yifan Chen, Yun Yang","submitted_at":"2021-03-09T05:57:08Z","abstract_excerpt":"Nystr\\\"om approximation is a fast randomized method that rapidly solves kernel ridge regression (KRR) problems through sub-sampling the n-by-n empirical kernel matrix appearing in the objective function. However, the performance of such a sub-sampling method heavily relies on correctly estimating the statistical leverage scores for forming the sampling distribution, which can be as costly as solving the original KRR. In this work, we propose a linear time (modulo poly-log terms) algorithm to accurately approximate the statistical leverage scores in the stationary-kernel-based KRR with theoreti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.05238","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/2103.05238/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:21:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pB3MPwh8jDYxiFPFHUy4DtEGvROcM7p8Wau7dmQuKxelKl7yY7DoV3bqAsHcwqCL4TCBEfonxfawNN5z+iucDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T20:12:35.348639Z"},"content_sha256":"4f5ce73262503428bd70a00fc302643c6d5c8203e45e752c6285078b87c065d3","schema_version":"1.0","event_id":"sha256:4f5ce73262503428bd70a00fc302643c6d5c8203e45e752c6285078b87c065d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCZTB5VE5UECJE3XTPAHAKDMNY/bundle.json","state_url":"https://pith.science/pith/VCZTB5VE5UECJE3XTPAHAKDMNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCZTB5VE5UECJE3XTPAHAKDMNY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T20:12:35Z","links":{"resolver":"https://pith.science/pith/VCZTB5VE5UECJE3XTPAHAKDMNY","bundle":"https://pith.science/pith/VCZTB5VE5UECJE3XTPAHAKDMNY/bundle.json","state":"https://pith.science/pith/VCZTB5VE5UECJE3XTPAHAKDMNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCZTB5VE5UECJE3XTPAHAKDMNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:VCZTB5VE5UECJE3XTPAHAKDMNY","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":"3ab2802366b3a8a7fe1647f9310e263dd7cb0007d03db756991074b0d5ea6374","cross_cats_sorted":["cs.LG","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-03-09T05:57:08Z","title_canon_sha256":"fba76dd21a12260b252b49cbc35feadb3452f3100484e014529eb07a4f8616af"},"schema_version":"1.0","source":{"id":"2103.05238","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.05238","created_at":"2026-07-05T02:21:24Z"},{"alias_kind":"arxiv_version","alias_value":"2103.05238v1","created_at":"2026-07-05T02:21:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.05238","created_at":"2026-07-05T02:21:24Z"},{"alias_kind":"pith_short_12","alias_value":"VCZTB5VE5UEC","created_at":"2026-07-05T02:21:24Z"},{"alias_kind":"pith_short_16","alias_value":"VCZTB5VE5UECJE3X","created_at":"2026-07-05T02:21:24Z"},{"alias_kind":"pith_short_8","alias_value":"VCZTB5VE","created_at":"2026-07-05T02:21:24Z"}],"graph_snapshots":[{"event_id":"sha256:4f5ce73262503428bd70a00fc302643c6d5c8203e45e752c6285078b87c065d3","target":"graph","created_at":"2026-07-05T02:21:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2103.05238/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Nystr\\\"om approximation is a fast randomized method that rapidly solves kernel ridge regression (KRR) problems through sub-sampling the n-by-n empirical kernel matrix appearing in the objective function. However, the performance of such a sub-sampling method heavily relies on correctly estimating the statistical leverage scores for forming the sampling distribution, which can be as costly as solving the original KRR. In this work, we propose a linear time (modulo poly-log terms) algorithm to accurately approximate the statistical leverage scores in the stationary-kernel-based KRR with theoreti","authors_text":"Yifan Chen, Yun Yang","cross_cats":["cs.LG","stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-03-09T05:57:08Z","title":"Fast Statistical Leverage Score Approximation in Kernel Ridge Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.05238","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":"sha256:3d48eb63834e4ed444419787a32c3c05e726af5ab800f127c78bb0dca19f8520","target":"record","created_at":"2026-07-05T02:21:24Z","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":"3ab2802366b3a8a7fe1647f9310e263dd7cb0007d03db756991074b0d5ea6374","cross_cats_sorted":["cs.LG","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2021-03-09T05:57:08Z","title_canon_sha256":"fba76dd21a12260b252b49cbc35feadb3452f3100484e014529eb07a4f8616af"},"schema_version":"1.0","source":{"id":"2103.05238","kind":"arxiv","version":1}},"canonical_sha256":"a8b330f6a4ed082493779bc070286c6e1e813ee9070732e90b063379c7537e32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8b330f6a4ed082493779bc070286c6e1e813ee9070732e90b063379c7537e32","first_computed_at":"2026-07-05T02:21:24.071151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:21:24.071151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mfyGTAb06Fjmyn0MM3utJnCwze2ELMELjPVWVS8nbIIp/nJurr27jqlZfcWChVtfqpiSkkTmH3IpM1CpgkvEAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:21:24.071613Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.05238","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d48eb63834e4ed444419787a32c3c05e726af5ab800f127c78bb0dca19f8520","sha256:4f5ce73262503428bd70a00fc302643c6d5c8203e45e752c6285078b87c065d3"],"state_sha256":"3e7458a5406d39c7b3fb453847efdeec9a2dff57db0d249fbe5f04e0a00b2428"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eMHvYQjAGvXoBcb+5UkjPCQ/euQRrX8pBuXUVCJgdW1qedQ9FOqvl7JahKIqSYn7mYYSfbjVHR4ia5qyaIN0BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T20:12:35.358998Z","bundle_sha256":"87bdf4cb6a94edf48ca39ca9425fd2800adaeabdc846d432d4001d929f6f91de"}}