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This research addresses a critical gap in probabilistic machine learning by establishing rigorous statistical confidence intervals for Expected Calibration Error. By accounting for distinct convergence rates between calibrated and miscalibrated models, the study provides more efficient evaluation metrics than traditional resampling methods. This advancement offers practitioners reliable tools to quantify uncertainty in model predictions without relying on computationally expensive bootstrapping techniques.
A Confidence Interval for the $\ell_2$ Expected Calibration Error
arXiv:2408.08998v4 Announce Type: replace-cross Abstract: Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model calibration, the rigorous statistical evaluation of model calibration remains less explored. In this work, we develop confidence intervals the $\ell_2$ Expected Calibration Error (ECE). We consider top-1-to-$k$ calibration, which includes both the popular notion of confidence calibration as well as full calibration. For a debiased estimator of the ECE, we show asymptotic normality, but with different convergence rates and asymptotic variances for calibrated and miscalibrated models. We develop methods to construct asymptotically valid confidence intervals for the ECE, accounting for this behavior as well as non-negativity. Our theoretical findings are supported through extensive experiments, showing that our methods produce valid confidence intervals with shorter lengths compared to those obtained by resampling-based methods.
Abstract:Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model calibration, the rigorous statistical evaluation of model calibration remains less explored. In this work, we develop confidence intervals the $\ell_2$ Expected Calibration Error (ECE). We consider top-1-to-$k$ calibration, which includes both the popular notion of confidence calibration as well as full calibration. For a debiased estimator of the ECE, we show asymptotic normality, but with different convergence rates and asymptotic variances for calibrated and miscalibrated models. We develop methods to construct asymptotically valid confidence intervals for the ECE, accounting for this behavior as well as non-negativity. Our theoretical findings are supported through extensive experiments, showing that our methods produce valid confidence intervals with shorter lengths compared to those obtained by resampling-based methods.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2408.08998 [stat.ML]
(or arXiv:2408.08998v4 [stat.ML] for this version)
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