Optimal and Provable Calibration in High-Dimensional Binary Classification: Angular Calibration and Platt Scaling

We study the fundamental problem of calibrating a linear binary classifier of the form σ(ˆw x), where the feature vector xis Gaussian, σis a link function, and ˆw is an estimator of the true linear weight w . By interpolating with a noninformative chance classifier, we construct a well-calibrated predictor whose interpolation weight depends on the angle (ˆw,w) between the estimator ˆw and the true linear weight w . We establish that this angular calibration approach is provably well-calibrated in a high-dimensional regime where the number of samples and features both diverge, at a comparable rate.