Bandwidth Selection in Kernel Density Estimation for Model Calibration
This work addresses the critical problem of reliable uncertainty estimation in high-stakes deep learning applications by improving calibration assessment.
The paper introduces Risk Alignment (RA), a novel optimization framework for bandwidth selection in Kernel Density Estimation (KDE) that aligns KDE-reconstructed risk with empirical risk, leading to more reliable calibration assessments. Experiments show RA consistently outperforms standard methods across multiple architectures and datasets.
As deep learning models are increasingly deployed in high-stakes applications, providing well-calibrated uncertainty estimates has become as critical as achieving high predictive accuracy. While Kernel Density Estimation (KDE) has emerged as a smooth and continuous alternative to traditional binning for quantifying miscalibration, its reliability is heavily dependent on the choice of the kernel bandwidth. Standard selection techniques, such as Maximum Likelihood Estimation (MLE), often fail to produce optimal bandwidths for calibration tasks. In this work, we introduce Risk Alignment (RA), a novel optimization framework that determines the optimal bandwidth by aligning KDE-reconstructed risk with empirical risk. We theoretically demonstrate that this alignment minimizes calibration estimation bias across the data distribution, establishing a principled bandwidth selection criterion applicable to various metrics, including the challenging case of canonical calibration error. Extensive experiments across multiple architectures and datasets show that RA consistently outperforms standard bandwidth selection methods, yielding more reliable calibration assessments.