{"paper":{"title":"Asymptotic Optimism of Random-Design Linear and Kernel Regression Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Hengrui Luo, Yunzhang Zhu","submitted_at":"2025-02-18T16:19:28Z","abstract_excerpt":"We derived the closed-form asymptotic optimism of linear regression models under random designs, and generalizes it to kernel ridge regression. Using scaled asymptotic optimism as a generic predictive model complexity measure, we studied the fundamental different behaviors of linear regression model, tangent kernel (NTK) regression model and three-layer fully connected neural networks (NN). Our contribution is two-fold: we provided theoretical ground for using scaled optimism as a model predictive complexity measure; and we show empirically that NN with ReLUs behaves differently from kernel mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.12999","kind":"arxiv","version":3},"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/2502.12999/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"}