{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RHHT25DJEIADJP6OKKO7CE66AM","short_pith_number":"pith:RHHT25DJ","canonical_record":{"source":{"id":"1912.13421","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-12-31T16:58:42Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"eb2e55634f4e5e895fe200e5fa59ffa9c9c599e93a9b59bb1a1d7c5a536021b5","abstract_canon_sha256":"b7ec90af106af7d1403b2e3dd729831c14882f722052752babdb6a4636542ca3"},"schema_version":"1.0"},"canonical_sha256":"89cf3d7469220034bfce529df113de0321cbb31a745c61b57cb9e628489c1b37","source":{"kind":"arxiv","id":"1912.13421","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.13421","created_at":"2026-07-05T00:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"1912.13421v2","created_at":"2026-07-05T00:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.13421","created_at":"2026-07-05T00:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"RHHT25DJEIAD","created_at":"2026-07-05T00:41:54Z"},{"alias_kind":"pith_short_16","alias_value":"RHHT25DJEIADJP6O","created_at":"2026-07-05T00:41:54Z"},{"alias_kind":"pith_short_8","alias_value":"RHHT25DJ","created_at":"2026-07-05T00:41:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RHHT25DJEIADJP6OKKO7CE66AM","target":"record","payload":{"canonical_record":{"source":{"id":"1912.13421","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-12-31T16:58:42Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"eb2e55634f4e5e895fe200e5fa59ffa9c9c599e93a9b59bb1a1d7c5a536021b5","abstract_canon_sha256":"b7ec90af106af7d1403b2e3dd729831c14882f722052752babdb6a4636542ca3"},"schema_version":"1.0"},"canonical_sha256":"89cf3d7469220034bfce529df113de0321cbb31a745c61b57cb9e628489c1b37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:41:54.211976Z","signature_b64":"HsY2h4aJ89G7650PGYdR2+58hbaO2dAYIfBsFKbSic8aqJKVcorFW1HbUhpntjrsOymQw4fZ6ibH2hNjlCtGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89cf3d7469220034bfce529df113de0321cbb31a745c61b57cb9e628489c1b37","last_reissued_at":"2026-07-05T00:41:54.211523Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:41:54.211523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.13421","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":"2026-07-05T00:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R6KtXSww5tg8Kq6XbMQ30AR8qWcw6sfiW1KrrWy/ycrbHACRUYQkrcAwTC8QqB4y9Z4Cpr3NdC7JV3i+uOZJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T13:31:15.564374Z"},"content_sha256":"3558c954370b9eeda2bdff11ac8409122153d1108104dabacd82648a93cc7e24","schema_version":"1.0","event_id":"sha256:3558c954370b9eeda2bdff11ac8409122153d1108104dabacd82648a93cc7e24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RHHT25DJEIADJP6OKKO7CE66AM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Risk of the Least Squares Minimum Norm Estimator under the Spike Covariance Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Yasaman Mahdaviyeh, Zacharie Naulet","submitted_at":"2019-12-31T16:58:42Z","abstract_excerpt":"We study risk of the minimum norm linear least squares estimator in when the number of parameters $d$ depends on $n$, and $\\frac{d}{n} \\rightarrow \\infty$. We assume that data has an underlying low rank structure by restricting ourselves to spike covariance matrices, where a fixed finite number of eigenvalues grow with $n$ and are much larger than the rest of the eigenvalues, which are (asymptotically) in the same order. We show that in this setting risk of minimum norm least squares estimator vanishes in compare to risk of the null estimator. We give asymptotic and non asymptotic upper bounds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.13421","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1912.13421/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":"2026-07-05T00:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBzzc5N8LeuYGNsWg308Duai5FFCtG+7dOtJ8uzg3ncybewLHtkI+E695NOI1MlPXassMvrxLM+GCu9ACNvNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T13:31:15.564752Z"},"content_sha256":"d569af5ec651e1e0d35c1ecfdac0d80a9ce246f0184dc0147cd386888386df58","schema_version":"1.0","event_id":"sha256:d569af5ec651e1e0d35c1ecfdac0d80a9ce246f0184dc0147cd386888386df58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHHT25DJEIADJP6OKKO7CE66AM/bundle.json","state_url":"https://pith.science/pith/RHHT25DJEIADJP6OKKO7CE66AM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHHT25DJEIADJP6OKKO7CE66AM/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":"2026-07-06T13:31:15Z","links":{"resolver":"https://pith.science/pith/RHHT25DJEIADJP6OKKO7CE66AM","bundle":"https://pith.science/pith/RHHT25DJEIADJP6OKKO7CE66AM/bundle.json","state":"https://pith.science/pith/RHHT25DJEIADJP6OKKO7CE66AM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHHT25DJEIADJP6OKKO7CE66AM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RHHT25DJEIADJP6OKKO7CE66AM","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":"b7ec90af106af7d1403b2e3dd729831c14882f722052752babdb6a4636542ca3","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-12-31T16:58:42Z","title_canon_sha256":"eb2e55634f4e5e895fe200e5fa59ffa9c9c599e93a9b59bb1a1d7c5a536021b5"},"schema_version":"1.0","source":{"id":"1912.13421","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.13421","created_at":"2026-07-05T00:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"1912.13421v2","created_at":"2026-07-05T00:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.13421","created_at":"2026-07-05T00:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"RHHT25DJEIAD","created_at":"2026-07-05T00:41:54Z"},{"alias_kind":"pith_short_16","alias_value":"RHHT25DJEIADJP6O","created_at":"2026-07-05T00:41:54Z"},{"alias_kind":"pith_short_8","alias_value":"RHHT25DJ","created_at":"2026-07-05T00:41:54Z"}],"graph_snapshots":[{"event_id":"sha256:d569af5ec651e1e0d35c1ecfdac0d80a9ce246f0184dc0147cd386888386df58","target":"graph","created_at":"2026-07-05T00:41:54Z","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/1912.13421/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study risk of the minimum norm linear least squares estimator in when the number of parameters $d$ depends on $n$, and $\\frac{d}{n} \\rightarrow \\infty$. We assume that data has an underlying low rank structure by restricting ourselves to spike covariance matrices, where a fixed finite number of eigenvalues grow with $n$ and are much larger than the rest of the eigenvalues, which are (asymptotically) in the same order. We show that in this setting risk of minimum norm least squares estimator vanishes in compare to risk of the null estimator. We give asymptotic and non asymptotic upper bounds","authors_text":"Yasaman Mahdaviyeh, Zacharie Naulet","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-12-31T16:58:42Z","title":"Risk of the Least Squares Minimum Norm Estimator under the Spike Covariance Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.13421","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":"sha256:3558c954370b9eeda2bdff11ac8409122153d1108104dabacd82648a93cc7e24","target":"record","created_at":"2026-07-05T00:41:54Z","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":"b7ec90af106af7d1403b2e3dd729831c14882f722052752babdb6a4636542ca3","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-12-31T16:58:42Z","title_canon_sha256":"eb2e55634f4e5e895fe200e5fa59ffa9c9c599e93a9b59bb1a1d7c5a536021b5"},"schema_version":"1.0","source":{"id":"1912.13421","kind":"arxiv","version":2}},"canonical_sha256":"89cf3d7469220034bfce529df113de0321cbb31a745c61b57cb9e628489c1b37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89cf3d7469220034bfce529df113de0321cbb31a745c61b57cb9e628489c1b37","first_computed_at":"2026-07-05T00:41:54.211523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:41:54.211523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HsY2h4aJ89G7650PGYdR2+58hbaO2dAYIfBsFKbSic8aqJKVcorFW1HbUhpntjrsOymQw4fZ6ibH2hNjlCtGBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:41:54.211976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.13421","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3558c954370b9eeda2bdff11ac8409122153d1108104dabacd82648a93cc7e24","sha256:d569af5ec651e1e0d35c1ecfdac0d80a9ce246f0184dc0147cd386888386df58"],"state_sha256":"c49ef7dc20982c50180174e6aa2c91ca1f730c59f100baebcaa685aa52ae24a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rMzopV583kss7Byw8pSIkCQ3W+pLGXanLUiSpmAFPSIP3Tj3GZCe+2Jrz99dFAeqKFshhb78tV5H/EGxbiKaBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T13:31:15.566736Z","bundle_sha256":"4e6bc5edeee0010e424e7944f74345361b820282da8f713c1ede3f971fe03778"}}