{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:Y3GDRVCFBS72PP2EPZCVCN55XT","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":"042aec388c5e324d3d8e8e79a6445189eaa5e5777dc2d07c66c8bdf26fd6445a","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2023-05-30T12:18:39Z","title_canon_sha256":"7180a1f47939ef887236f3662282ebdc114f44b013abd632913c81f44351f56d"},"schema_version":"1.0","source":{"id":"2305.18974","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.18974","created_at":"2026-07-05T08:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"2305.18974v2","created_at":"2026-07-05T08:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.18974","created_at":"2026-07-05T08:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"Y3GDRVCFBS72","created_at":"2026-07-05T08:34:54Z"},{"alias_kind":"pith_short_16","alias_value":"Y3GDRVCFBS72PP2E","created_at":"2026-07-05T08:34:54Z"},{"alias_kind":"pith_short_8","alias_value":"Y3GDRVCF","created_at":"2026-07-05T08:34:54Z"}],"graph_snapshots":[{"event_id":"sha256:54f9c2015abd48d5c1436a49a0df6bb33f2aa39d3f60931bef60b1cd0c796228","target":"graph","created_at":"2026-07-05T08:34:54Z","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/2305.18974/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study robust linear regression in high-dimension, when both the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\\alpha=n/d$, and study a data model that includes outliers. We provide exact asymptotics for the performances of the empirical risk minimisation (ERM) using $\\ell_2$-regularised $\\ell_2$, $\\ell_1$, and Huber losses, which are the standard approach to such problems. We focus on two metrics for the performance: the generalisation error to similar datasets with outliers, and the estimation error of the original, unpolluted function. Our results are compare","authors_text":"Emanuele Troiani, Florent Krzakala, Matteo Vilucchio, Vittorio Erba","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2023-05-30T12:18:39Z","title":"Asymptotic Characterisation of Robust Empirical Risk Minimisation Performance in the Presence of Outliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.18974","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":"sha256:68cb7e2ae3ec93b274976808cc71d9958bd99ff4cceafd2b0317b96805292568","target":"record","created_at":"2026-07-05T08:34:54Z","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":"042aec388c5e324d3d8e8e79a6445189eaa5e5777dc2d07c66c8bdf26fd6445a","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2023-05-30T12:18:39Z","title_canon_sha256":"7180a1f47939ef887236f3662282ebdc114f44b013abd632913c81f44351f56d"},"schema_version":"1.0","source":{"id":"2305.18974","kind":"arxiv","version":2}},"canonical_sha256":"c6cc38d4450cbfa7bf447e455137bdbce8b979fac3cdf4b51493365f3d6b02a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6cc38d4450cbfa7bf447e455137bdbce8b979fac3cdf4b51493365f3d6b02a7","first_computed_at":"2026-07-05T08:34:54.905499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:34:54.905499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5UrIYP3xQwhmPw7nh1yO9iQN5n5v3RP7VixobK8ePSwplVPOnoT2vMFuoGlhruqkHXB5mMcSQ6rMxn9pLCvKCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:34:54.905933Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.18974","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68cb7e2ae3ec93b274976808cc71d9958bd99ff4cceafd2b0317b96805292568","sha256:54f9c2015abd48d5c1436a49a0df6bb33f2aa39d3f60931bef60b1cd0c796228"],"state_sha256":"d2fb5edd02ca91998948d0b72cddec71bef0d552ebc0ccb5d367b642f194a1b7"}