Regression methods are fundamental for scientific and technological
applications. However, fitted models can be highly unreliable outside of their
training domain, and hence the quantification of their uncertainty is crucial
in many of their applications. Based on the solution of a constrained
optimization problem, we propose "prediction rigidities" as a method to obtain
uncertainties of arbitrary pre-trained regressors. We establish a strong
connection between our framework and Bayesian inference, and we develop a
last-layer approximation that allows the new method to be applied to neural
networks. This extension affords cheap uncertainties without any modification
to the neural network itself or its training procedure. We show the
effectiveness of our method on a wide range of regression tasks, ranging from
simple toy models to applications in chemistry and meteorology.

基于约束优化问题的解决方案，我们提出 “预测刚性” 作为一种获取任意预训练回归器的不确定性的方法，并建立了我们的框架与贝叶斯推理之间的强连接。我们还开发了一种最后一层逼近，使得这种方法可以应用于神经网络，并且不需要对神经网络本身或其训练过程进行任何修改。我们在从简单玩具模型到化学和气象学应用的各种回归任务中展示了我们方法的有效性。