aiqbench analysis
This research establishes a provably well-calibrated linear binary classifier in high-dimensional regimes by leveraging the angle between estimator and true weights. The approach is uniquely Bregman-optimal and demonstrates that classical Platt scaling inherits these optimality properties under specific convergence conditions. For practitioners, this offers a theoretically grounded method to ensure calibration reliability when sample and feature counts diverge at comparable rates.
Optimal and Provable Calibration in High-Dimensional Binary Classification: Angular Calibration and Platt Scaling
arXiv:2502.15131v4 Announce Type: replace-cross Abstract: 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-dimensional regime where the number of samples and features both diverge, at a comparable rate. The angle $\angle(\hat{w}, w_\star)$ can be consistently estimated. Furthermore, the resulting predictor is uniquely $\textit{Bregman-optimal}$, minimizing the Bregman divergence to the true label distribution within a suitable class of calibrated predictors. Our work is the first to provide a calibration strategy that satisfies both calibration and optimality properties provably in high dimensions. Additionally, we identify conditions under which a classical Platt-scaling predictor converges to our Bregman-optimal calibrated solution. Thus, Platt-scaling also inherits these desirable properties provably in high dimensions.
Abstract: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-dimensional regime where the number of samples and features both diverge, at a comparable rate. The angle $\angle(\hat{w}, w_\star)$ can be consistently estimated. Furthermore, the resulting predictor is uniquely $\textit{Bregman-optimal}$, minimizing the Bregman divergence to the true label distribution within a suitable class of calibrated predictors. Our work is the first to provide a calibration strategy that satisfies both calibration and optimality properties provably in high dimensions. Additionally, we identify conditions under which a classical Platt-scaling predictor converges to our Bregman-optimal calibrated solution. Thus, Platt-scaling also inherits these desirable properties provably in high dimensions.
Statistics Theory (math.ST); Machine Learning (cs.LG); Methodology (stat.ME); Machine Learning (stat.ML)
arXiv:2502.15131 [math.ST]
(or arXiv:2502.15131v4 [math.ST] for this version)
From: Yufan Li Dr. [view email] [v1] Fri, 21 Feb 2025 01:24:27 UTC (151 KB) [v2] Sat, 27 Sep 2025 05:56:20 UTC (191 KB) [v3] Thu, 2 Oct 2025 03:20:06 UTC (191 KB) [v4] Sun, 7 Jun 2026 15:55:48 UTC (227 KB)
Full text under the publisher's open licence · 237 words