While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees and can be miscalibrated in practice. State-of-the-art approaches for designing calibrated models rely on inflating the Gaussian process posterior variance, which yields confidence intervals that are potentially too coarse. To remedy this, we present a calibration approach that generates predictive quantiles using a computation inspired by the vanilla Gaussian process posterior variance but using a different set of hyperparameters chosen to satisfy an empirical calibration constraint. This results in a calibration approach that is considerably more flexible than existing approaches, which we optimize to yield tight predictive quantiles. Our approach is shown to yield a calibrated model under reasonable assumptions. Furthermore, it outperforms existing approaches in sharpness when employed for calibrated regression.

翻译：尽管高斯过程是各种工程与科学应用中的主流方法，但其不确定性估计不满足频率学派保证，且在实践中可能失准。现有设计校准模型的前沿方法依赖于膨胀高斯过程后验方差，这会产生可能过于粗糙的置信区间。为解决此问题，我们提出一种校准方法，该方法采用受标准高斯过程后验方差启发的计算方式生成预测分位数，但使用一组满足经验校准约束的不同超参数。这使得校准方法比现有方法具有显著更高的灵活性，我们通过优化方法获得紧凑的预测分位数。我们的方法在合理假设下能够产生校准模型。此外，在校准回归应用中，该方法在尖峰性方面优于现有方法。