{"paper":{"title":"piCholesky: Polynomial Interpolation of Multiple Cholesky Factors for Efficient Approximate Cross-Validation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"cs.LG","authors_text":"Alex Gittens, Da Kuang, Raffay Hamid","submitted_at":"2014-04-02T05:33:41Z","abstract_excerpt":"The dominant cost in solving least-square problems using Newton's method is often that of factorizing the Hessian matrix over multiple values of the regularization parameter ($\\lambda$). We propose an efficient way to interpolate the Cholesky factors of the Hessian matrix computed over a small set of $\\lambda$ values. This approximation enables us to optimally minimize the hold-out error while incurring only a fraction of the cost compared to exact cross-validation. We provide a formal error bound for our approximation scheme and present solutions to a set of key implementation challenges that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0466","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":""},"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"}