论文标题
量化不确定性质量的结构和分布度量：评估高斯过程，深神经网和深神经操作员的回归
Structure and Distribution Metric for Quantifying the Quality of Uncertainty: Assessing Gaussian Processes, Deep Neural Nets, and Deep Neural Operators for Regression
论文作者
论文摘要
我们提出了两个有限的比较指标，这些指标可以实施到回归任务中的任意维度。一个量化了不确定性的结构，另一个量化了不确定性的分布。结构度量与真实误差评估了不确定性的形状和位置相似性，而分布度量标准量化了两者之间的受支持大小。我们将这些指标应用于高斯深神经网（DNN）和集合深神经操作员（DNOS）上，将这些指标应用于高维和非线性验证案例。我们发现，将模型的不确定性估计与模型的平方错误进行比较提供了令人信服的地面真相评估。我们还观察到，DNN和DNO，尤其是与GPS相比，均具有稀疏或丰富数据的高度指标。
We propose two bounded comparison metrics that may be implemented to arbitrary dimensions in regression tasks. One quantifies the structure of uncertainty and the other quantifies the distribution of uncertainty. The structure metric assesses the similarity in shape and location of uncertainty with the true error, while the distribution metric quantifies the supported magnitudes between the two. We apply these metrics to Gaussian Processes (GPs), Ensemble Deep Neural Nets (DNNs), and Ensemble Deep Neural Operators (DNOs) on high-dimensional and nonlinear test cases. We find that comparing a model's uncertainty estimates with the model's squared error provides a compelling ground truth assessment. We also observe that both DNNs and DNOs, especially when compared to GPs, provide encouraging metric values in high dimensions with either sparse or plentiful data.
