{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AY62QNBC2WTIUVVOGXIAFN7AKM","short_pith_number":"pith:AY62QNBC","canonical_record":{"source":{"id":"1502.06291","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-23T00:18:47Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"1eb133565ccec33d8063733067cf2b6ad56e9b74653aef89ba9fed9a5fa30c61","abstract_canon_sha256":"a3c2286b88ebcc756d9a81d67b7b79226e9701156a33aa3238ae67d44af99959"},"schema_version":"1.0"},"canonical_sha256":"063da83422d5a68a56ae35d002b7e0531b78270dc915a04baad5ef60e9d6c2a0","source":{"kind":"arxiv","id":"1502.06291","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06291","created_at":"2026-05-18T01:06:29Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06291v2","created_at":"2026-05-18T01:06:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06291","created_at":"2026-05-18T01:06:29Z"},{"alias_kind":"pith_short_12","alias_value":"AY62QNBC2WTI","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"AY62QNBC2WTIUVVO","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"AY62QNBC","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AY62QNBC2WTIUVVOGXIAFN7AKM","target":"record","payload":{"canonical_record":{"source":{"id":"1502.06291","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-23T00:18:47Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"1eb133565ccec33d8063733067cf2b6ad56e9b74653aef89ba9fed9a5fa30c61","abstract_canon_sha256":"a3c2286b88ebcc756d9a81d67b7b79226e9701156a33aa3238ae67d44af99959"},"schema_version":"1.0"},"canonical_sha256":"063da83422d5a68a56ae35d002b7e0531b78270dc915a04baad5ef60e9d6c2a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:29.303304Z","signature_b64":"DgmGeC6kFVFecbeWLVUporSisZaf1m1cFG2juHwEdidDGjrcEMJufxqCxDuqddNEiqR6ucjFW5eDtCTmTDRbCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"063da83422d5a68a56ae35d002b7e0531b78270dc915a04baad5ef60e9d6c2a0","last_reissued_at":"2026-05-18T01:06:29.302696Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:29.302696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.06291","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LSRACnrVh4Mg4s/0oZNLA3Cpu97uln2rc6WEe9jaUfB0ErxYI6pr9igDXC5JROYnEK7vyaIgB3N/IG29U+9lCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T02:32:28.920498Z"},"content_sha256":"004f968c51c35d4aa184e1825a27a8d87a2c643d56cac6451421f70def70527d","schema_version":"1.0","event_id":"sha256:004f968c51c35d4aa184e1825a27a8d87a2c643d56cac6451421f70def70527d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AY62QNBC2WTIUVVOGXIAFN7AKM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Prediction error of cross-validated Lasso","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Jafar Jafarov, Sourav Chatterjee","submitted_at":"2015-02-23T00:18:47Z","abstract_excerpt":"In spite of the wealth of literature on the theoretical properties of the Lasso, there is very little known when the value of the tuning parameter is chosen using the data, even though this is what actually happens in practice. We give a general upper bound on the prediction error of Lasso when the tuning parameter is chosen using a variant of 2-fold cross-validation. No special assumption is made about the structure of the design matrix, and the tuning parameter is allowed to be optimized over an arbitrary data-dependent set of values. The proof is based on a general principle that may extend"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06291","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"24xTwMvfTh006chwIbMJNVK3tWY84TXL8CSkrzG6Q0ArsGTpICb16RW9i2zBrgX0fVEZlukpyfhtg0xLSIDhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T02:32:28.920845Z"},"content_sha256":"98e2ce76734f4970935880f343487d2e39ef9e6fd4b7fa8b104f8e46598b4284","schema_version":"1.0","event_id":"sha256:98e2ce76734f4970935880f343487d2e39ef9e6fd4b7fa8b104f8e46598b4284"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AY62QNBC2WTIUVVOGXIAFN7AKM/bundle.json","state_url":"https://pith.science/pith/AY62QNBC2WTIUVVOGXIAFN7AKM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AY62QNBC2WTIUVVOGXIAFN7AKM/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":"2026-05-22T02:32:28Z","links":{"resolver":"https://pith.science/pith/AY62QNBC2WTIUVVOGXIAFN7AKM","bundle":"https://pith.science/pith/AY62QNBC2WTIUVVOGXIAFN7AKM/bundle.json","state":"https://pith.science/pith/AY62QNBC2WTIUVVOGXIAFN7AKM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AY62QNBC2WTIUVVOGXIAFN7AKM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AY62QNBC2WTIUVVOGXIAFN7AKM","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":"a3c2286b88ebcc756d9a81d67b7b79226e9701156a33aa3238ae67d44af99959","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-23T00:18:47Z","title_canon_sha256":"1eb133565ccec33d8063733067cf2b6ad56e9b74653aef89ba9fed9a5fa30c61"},"schema_version":"1.0","source":{"id":"1502.06291","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06291","created_at":"2026-05-18T01:06:29Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06291v2","created_at":"2026-05-18T01:06:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06291","created_at":"2026-05-18T01:06:29Z"},{"alias_kind":"pith_short_12","alias_value":"AY62QNBC2WTI","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"AY62QNBC2WTIUVVO","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"AY62QNBC","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:98e2ce76734f4970935880f343487d2e39ef9e6fd4b7fa8b104f8e46598b4284","target":"graph","created_at":"2026-05-18T01:06:29Z","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 spite of the wealth of literature on the theoretical properties of the Lasso, there is very little known when the value of the tuning parameter is chosen using the data, even though this is what actually happens in practice. We give a general upper bound on the prediction error of Lasso when the tuning parameter is chosen using a variant of 2-fold cross-validation. No special assumption is made about the structure of the design matrix, and the tuning parameter is allowed to be optimized over an arbitrary data-dependent set of values. The proof is based on a general principle that may extend","authors_text":"Jafar Jafarov, Sourav Chatterjee","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-23T00:18:47Z","title":"Prediction error of cross-validated Lasso"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06291","kind":"arxiv","version":2},"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":"sha256:004f968c51c35d4aa184e1825a27a8d87a2c643d56cac6451421f70def70527d","target":"record","created_at":"2026-05-18T01:06:29Z","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":"a3c2286b88ebcc756d9a81d67b7b79226e9701156a33aa3238ae67d44af99959","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-02-23T00:18:47Z","title_canon_sha256":"1eb133565ccec33d8063733067cf2b6ad56e9b74653aef89ba9fed9a5fa30c61"},"schema_version":"1.0","source":{"id":"1502.06291","kind":"arxiv","version":2}},"canonical_sha256":"063da83422d5a68a56ae35d002b7e0531b78270dc915a04baad5ef60e9d6c2a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"063da83422d5a68a56ae35d002b7e0531b78270dc915a04baad5ef60e9d6c2a0","first_computed_at":"2026-05-18T01:06:29.302696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:29.302696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DgmGeC6kFVFecbeWLVUporSisZaf1m1cFG2juHwEdidDGjrcEMJufxqCxDuqddNEiqR6ucjFW5eDtCTmTDRbCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:29.303304Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06291","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:004f968c51c35d4aa184e1825a27a8d87a2c643d56cac6451421f70def70527d","sha256:98e2ce76734f4970935880f343487d2e39ef9e6fd4b7fa8b104f8e46598b4284"],"state_sha256":"cf04f6ce4420d584717e2a6d761f8ad0aaeeb67bec48c3a0f30bb3f9f733c24c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Hv3MqJIg77ElCCk8FsUZkT1yPMgBmIlBkSvczMg8PjS01jOo7KT8b0h/ihTxEbr4R1D65RTSZgOpP163zhrCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T02:32:28.924147Z","bundle_sha256":"4ce13ead847ac3af559ae1f90a73f8e47c1bf185e6b654f6336560b0ed61de9f"}}