{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:WP6DU432Y6ZBAR3JR5JTPTT7NI","short_pith_number":"pith:WP6DU432","canonical_record":{"source":{"id":"1001.0188","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-12-31T22:10:59Z","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"title_canon_sha256":"d7d33e2f9cc08fd0f182c61406b0b8d27f1164527340203387e69d4cb44e4fd0","abstract_canon_sha256":"d5d090138a1b53a17f6414558e51cb47abf557a59fcc961b52319369c9d228b1"},"schema_version":"1.0"},"canonical_sha256":"b3fc3a737ac7b21047698f5337ce7f6a3e927b41e72449e387d9300e23b0d88e","source":{"kind":"arxiv","id":"1001.0188","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0188","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0188v5","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0188","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"pith_short_12","alias_value":"WP6DU432Y6ZB","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"WP6DU432Y6ZBAR3J","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"WP6DU432","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:WP6DU432Y6ZBAR3JR5JTPTT7NI","target":"record","payload":{"canonical_record":{"source":{"id":"1001.0188","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-12-31T22:10:59Z","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"title_canon_sha256":"d7d33e2f9cc08fd0f182c61406b0b8d27f1164527340203387e69d4cb44e4fd0","abstract_canon_sha256":"d5d090138a1b53a17f6414558e51cb47abf557a59fcc961b52319369c9d228b1"},"schema_version":"1.0"},"canonical_sha256":"b3fc3a737ac7b21047698f5337ce7f6a3e927b41e72449e387d9300e23b0d88e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:26.226914Z","signature_b64":"XjjlTFENJG92FdoC+FloBRcpu/fBzdZ5N5dbjp2rSQmXTmrIU0ZKJf9MBUcQ49xOPf2a2C3GsMsJy8ObcdhHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3fc3a737ac7b21047698f5337ce7f6a3e927b41e72449e387d9300e23b0d88e","last_reissued_at":"2026-05-18T03:30:26.226255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:26.226255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.0188","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:30:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Na6Ipb0t3PLeSwnytVKHBoh3qNvWPjG8qwfKd30NNXGURMPJfYipcn8j9W1jxo8+VYbDAs75W/lcMAFCOO9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:05:19.584105Z"},"content_sha256":"c90bea6a15564e80282be719579a29a7799e4c44f3bff552dabd1e833b7a0de4","schema_version":"1.0","event_id":"sha256:c90bea6a15564e80282be719579a29a7799e4c44f3bff552dabd1e833b7a0de4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:WP6DU432Y6ZBAR3JR5JTPTT7NI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Least squares after model selection in high-dimensional sparse models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Alexandre Belloni, Victor Chernozhukov","submitted_at":"2009-12-31T22:10:59Z","abstract_excerpt":"In this article we study post-model selection estimators that apply ordinary least squares (OLS) to the model selected by first-step penalized estimators, typically Lasso. It is well known that Lasso can estimate the nonparametric regression function at nearly the oracle rate, and is thus hard to improve upon. We show that the OLS post-Lasso estimator performs at least as well as Lasso in terms of the rate of convergence, and has the advantage of a smaller bias. Remarkably, this performance occurs even if the Lasso-based model selection \"fails\" in the sense of missing some components of the \"t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0188","kind":"arxiv","version":5},"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":"2026-05-18T03:30:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/40kGFixf3NDZ12VupEpD+I2eHPinhD1wBwESPN6x4nwOdppH7rBbAOGzzHFTQZvrBIHfTUlYdFA3bxDQbt1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T03:05:19.584620Z"},"content_sha256":"1ad79d13448b84366e0e37acd23c78fd7bb5fb7f3be3c6543afe0fdbbc3f9497","schema_version":"1.0","event_id":"sha256:1ad79d13448b84366e0e37acd23c78fd7bb5fb7f3be3c6543afe0fdbbc3f9497"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WP6DU432Y6ZBAR3JR5JTPTT7NI/bundle.json","state_url":"https://pith.science/pith/WP6DU432Y6ZBAR3JR5JTPTT7NI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WP6DU432Y6ZBAR3JR5JTPTT7NI/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":"2026-05-25T03:05:19Z","links":{"resolver":"https://pith.science/pith/WP6DU432Y6ZBAR3JR5JTPTT7NI","bundle":"https://pith.science/pith/WP6DU432Y6ZBAR3JR5JTPTT7NI/bundle.json","state":"https://pith.science/pith/WP6DU432Y6ZBAR3JR5JTPTT7NI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WP6DU432Y6ZBAR3JR5JTPTT7NI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:WP6DU432Y6ZBAR3JR5JTPTT7NI","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":"d5d090138a1b53a17f6414558e51cb47abf557a59fcc961b52319369c9d228b1","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-12-31T22:10:59Z","title_canon_sha256":"d7d33e2f9cc08fd0f182c61406b0b8d27f1164527340203387e69d4cb44e4fd0"},"schema_version":"1.0","source":{"id":"1001.0188","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0188","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0188v5","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0188","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"pith_short_12","alias_value":"WP6DU432Y6ZB","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"WP6DU432Y6ZBAR3J","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"WP6DU432","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:1ad79d13448b84366e0e37acd23c78fd7bb5fb7f3be3c6543afe0fdbbc3f9497","target":"graph","created_at":"2026-05-18T03:30:26Z","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 this article we study post-model selection estimators that apply ordinary least squares (OLS) to the model selected by first-step penalized estimators, typically Lasso. It is well known that Lasso can estimate the nonparametric regression function at nearly the oracle rate, and is thus hard to improve upon. We show that the OLS post-Lasso estimator performs at least as well as Lasso in terms of the rate of convergence, and has the advantage of a smaller bias. Remarkably, this performance occurs even if the Lasso-based model selection \"fails\" in the sense of missing some components of the \"t","authors_text":"Alexandre Belloni, Victor Chernozhukov","cross_cats":["math.PR","stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-12-31T22:10:59Z","title":"Least squares after model selection in high-dimensional sparse models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0188","kind":"arxiv","version":5},"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:c90bea6a15564e80282be719579a29a7799e4c44f3bff552dabd1e833b7a0de4","target":"record","created_at":"2026-05-18T03:30:26Z","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":"d5d090138a1b53a17f6414558e51cb47abf557a59fcc961b52319369c9d228b1","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-12-31T22:10:59Z","title_canon_sha256":"d7d33e2f9cc08fd0f182c61406b0b8d27f1164527340203387e69d4cb44e4fd0"},"schema_version":"1.0","source":{"id":"1001.0188","kind":"arxiv","version":5}},"canonical_sha256":"b3fc3a737ac7b21047698f5337ce7f6a3e927b41e72449e387d9300e23b0d88e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3fc3a737ac7b21047698f5337ce7f6a3e927b41e72449e387d9300e23b0d88e","first_computed_at":"2026-05-18T03:30:26.226255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:26.226255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XjjlTFENJG92FdoC+FloBRcpu/fBzdZ5N5dbjp2rSQmXTmrIU0ZKJf9MBUcQ49xOPf2a2C3GsMsJy8ObcdhHAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:26.226914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.0188","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c90bea6a15564e80282be719579a29a7799e4c44f3bff552dabd1e833b7a0de4","sha256:1ad79d13448b84366e0e37acd23c78fd7bb5fb7f3be3c6543afe0fdbbc3f9497"],"state_sha256":"22c3746c64b2f9842e0e8f9e025cba6de061d4860f2e140cdc44ec74d558779f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pBNN5jfKjGwTib/CfgqHJmIQOHRr2SXKdYjd35Y2npF0+mbpWTCmaUTK36zWfE8+4TBFgO/+XI9noN/MCaY6BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T03:05:19.588514Z","bundle_sha256":"da8123006a29bb9ad6ffe0d5762d96b25ad6611596bb1a3cb047e01177a345b0"}}