{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WHLH2L6LNKTRCH7QJLVCQBM5SU","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":"50771aac98f9af76a5e5ed12e795e3be339a96eec6f5b2da8f05564eec316478","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-03-25T13:35:02Z","title_canon_sha256":"96f39a7ac7caf255eaa595c1cb7564ee5ed41e4ec487c413bf8b8e0d13758f49"},"schema_version":"1.0","source":{"id":"1003.4885","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4885","created_at":"2026-05-18T04:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4885v2","created_at":"2026-05-18T04:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4885","created_at":"2026-05-18T04:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"WHLH2L6LNKTR","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WHLH2L6LNKTRCH7Q","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WHLH2L6L","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:58484e7169b96c73abac4206bb71f896c7b8291d0d2436e0054d1e4aa130f52b","target":"graph","created_at":"2026-05-18T04:11:18Z","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":"We consider a linear regression problem in a high dimensional setting where the number of covariates $p$ can be much larger than the sample size $n$. In such a situation, one often assumes sparsity of the regression vector, \\textit i.e., the regression vector contains many zero components. We propose a Lasso-type estimator $\\hat{\\beta}^{Quad}$ (where '$Quad$' stands for quadratic) which is based on two penalty terms. The first one is the $\\ell_1$ norm of the regression coefficients used to exploit the sparsity of the regression as done by the Lasso estimator, whereas the second is a quadratic ","authors_text":"Mohamed Hebiri, Sara A. van de Geer","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-03-25T13:35:02Z","title":"The Smooth-Lasso and other $\\ell_1+\\ell_2$-penalized methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4885","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:a38e544b0ef67f0bba2ef110f3fbe08698bf091a86bb10a5e038955e416655fc","target":"record","created_at":"2026-05-18T04:11:18Z","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":"50771aac98f9af76a5e5ed12e795e3be339a96eec6f5b2da8f05564eec316478","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-03-25T13:35:02Z","title_canon_sha256":"96f39a7ac7caf255eaa595c1cb7564ee5ed41e4ec487c413bf8b8e0d13758f49"},"schema_version":"1.0","source":{"id":"1003.4885","kind":"arxiv","version":2}},"canonical_sha256":"b1d67d2fcb6aa7111ff04aea28059d9521152cd81d6301489d840789fe45ec66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1d67d2fcb6aa7111ff04aea28059d9521152cd81d6301489d840789fe45ec66","first_computed_at":"2026-05-18T04:11:18.090088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:18.090088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xjKwDgtefvmHGif2S8DJAdnpHPvOnvdqDvWAIYTFcV7E7azhR0tM/Z1E6Wfj3aU/DLyULjnZjUX+Ycbz3W3dAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:18.090716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.4885","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a38e544b0ef67f0bba2ef110f3fbe08698bf091a86bb10a5e038955e416655fc","sha256:58484e7169b96c73abac4206bb71f896c7b8291d0d2436e0054d1e4aa130f52b"],"state_sha256":"082358b7bc93af46378ecba0c02b3f77105c2711d5e3f58cd1779dda291432d0"}