{"paper":{"title":"Robust, randomized preconditioning for kernel ridge regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Ethan N. Epperly, Joel A. Tropp, Mateo D\\'iaz, Robert J. Webber, Zachary Frangella","submitted_at":"2023-04-24T21:48:24Z","abstract_excerpt":"We investigate preconditioned conjugate gradient methods for kernel ridge regression (KRR) problems with a moderate to large number of data points ($10^4 \\leq N \\leq 10^7$). We develop and analyze two randomized preconditioners with complementary guarantees. For full-data KRR, RPCholesky preconditioning requires $O(N^2)$ arithmetic operations to achieve fixed accuracy under sufficiently rapid eigenvalue decay of the kernel matrix. For restricted KRR with $k\\ll N$ centers, KRILL preconditioning requires $O((N+k^2)k\\log k)$ operations with no eigenvalue-decay assumption. Experiments on benchmark"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.12465","kind":"arxiv","version":6},"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/2304.12465/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"}