{"paper":{"title":"Optimal and Provable Calibration in High-Dimensional Binary Classification: Angular Calibration and Platt Scaling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Pragya Sur, Yufan Li","submitted_at":"2025-02-21T01:24:27Z","abstract_excerpt":"We study the fundamental problem of calibrating a linear binary classifier of the form $\\sigma(\\hat{w}^\\top x)$, where the feature vector $x$ is Gaussian, $\\sigma$ is a link function, and $\\hat{w}$ is an estimator of the true linear weight $w^\\star$. By interpolating with a noninformative $\\textit{chance classifier}$, we construct a well-calibrated predictor whose interpolation weight depends on the angle $\\angle(\\hat{w}, w_\\star)$ between the estimator $\\hat{w}$ and the true linear weight $w_\\star$. We establish that this angular calibration approach is provably well-calibrated in a high-dime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.15131","kind":"arxiv","version":4},"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/2502.15131/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"}