Probabilistic regression models typically use the Maximum Likelihood Estimation or Cross-Validation to fit parameters. These methods can give an advantage to the solutions that fit observations on average, but they do not pay attention to the coverage and the width of Prediction Intervals. A robust two-step approach is used to address the problem of adjusting and calibrating Prediction Intervals for Gaussian Processes Regression. First, the covariance hyperparameters are determined by a standard Cross-Validation or Maximum Likelihood Estimation method. A Leave-One-Out Coverage Probability is introduced as a metric to adjust the covariance hyperparameters and assess the optimal type II Coverage Probability to a nominal level. Then a relaxation method is applied to choose the hyperparameters that minimize the Wasserstein distance between the Gaussian distribution with the initial hyperparameters (obtained by Cross-Validation or Maximum Likelihood Estimation) and the proposed Gaussian distribution with the hyperparameters that achieve the desired Coverage Probability. The method gives Prediction Intervals with appropriate coverage probabilities and small widths.
翻译:概率回归模型通常使用最大似值估计或跨度估计法来适应参数。 这些方法能够给符合平均观测结果的解决方案带来优势, 但不会注意预测间间隔的覆盖范围和宽度。 采用了稳健的两步方法来解决高斯进程回归时调整和校准预测间距的问题。 首先, 共差超参数由标准的跨度估计法或最大似差估计法确定。 引入了“ 留位- 一次性覆盖”概率,作为调整常数双参数和评估最佳的第二类覆盖范围可达到名义水平的尺度。 然后, 采用放松法来选择能够将高斯分布与初始超参数(跨度或最大似度估计法)之间的瓦塞尔斯坦距离最小化的超参数, 以及拟议的高斯分布与达到理想范围可测度的适当超参数的超值参数相匹配, 从而实现预期范围的宽度。 该方法提供了预测性和宽度。