Calibration by Distribution Matching: Trainable Kernel Calibration Metrics

• URL: http://arxiv.org/abs/2310.20211v1
• Date: Tue, 31 Oct 2023 06:19:40 GMT
• Title: Calibration by Distribution Matching: Trainable Kernel Calibration Metrics
• Authors: Charles Marx, Sofian Zalouk, Stefano Ermon
• Abstract summary: We introduce kernel-based calibration metrics that unify and generalize popular forms of calibration for both classification and regression. These metrics admit differentiable sample estimates, making it easy to incorporate a calibration objective into empirical risk minimization. We provide intuitive mechanisms to tailor calibration metrics to a decision task, and enforce accurate loss estimation and no regret decisions.
• Score: 56.629245030893685
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Calibration ensures that probabilistic forecasts meaningfully capture uncertainty by requiring that predicted probabilities align with empirical frequencies. However, many existing calibration methods are specialized for post-hoc recalibration, which can worsen the sharpness of forecasts. Drawing on the insight that calibration can be viewed as a distribution matching task, we introduce kernel-based calibration metrics that unify and generalize popular forms of calibration for both classification and regression. These metrics admit differentiable sample estimates, making it easy to incorporate a calibration objective into empirical risk minimization. Furthermore, we provide intuitive mechanisms to tailor calibration metrics to a decision task, and enforce accurate loss estimation and no regret decisions. Our empirical evaluation demonstrates that employing these metrics as regularizers enhances calibration, sharpness, and decision-making across a range of regression and classification tasks, outperforming methods relying solely on post-hoc recalibration.

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