结合共形预测的高斯过程插值：方法与比较分析
Gaussian process interpolation with conformal prediction: methods and comparative analysis
AI总结：
针对高斯过程插值预测区间校准性不佳的问题，引入共形预测方法进行区间调整，提出非对称得分的新变体，实验验证其在不损失精度的前提下提升校准效果，推动该方法在高斯过程领域的应用。
摘要：
本文倡导将共形预测（conformal prediction, CP）方法用于高斯过程（Gaussian process, GP）插值，以提升预测区间的校准性。我们首先说明，采用经极大似然法选择参数的GP模型，其预测通常无法达到最优校准效果。CP方法可调整预测区间，在保留底层GP模型精度的同时实现更优的不确定性量化。我们对比了多种CP变体，并提出一种基于非对称得分的全新变体。数值实验表明，CP方法可在不损失精度的前提下有效提升校准性。本研究旨在推动CP方法在GP研究领域的应用。
英文摘要：
This article advocates the use of conformal prediction (CP) methods for Gaussian process (GP) interpolation to enhance the calibration of prediction intervals. We begin by illustrating that using a GP model with parameters selected by maximum likelihood often results in predictions that are not optimally calibrated. CP methods can adjust the prediction intervals, leading to better uncertainty quantification while maintaining the accuracy of the underlying GP model. We compare different CP variants and introduce a novel variant based on an asymmetric score. Our numerical experiments demonstrate the effectiveness of CP methods in improving calibration without compromising accuracy. This work aims to facilitate the adoption of CP methods in the GP community.
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