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.

翻译：回归方法在科学与技术应用中至关重要。然而，拟合模型在其训练领域之外可能高度不可靠，因此量化其不确定性在众多应用中十分关键。基于约束优化问题的求解，我们提出"预测刚性"作为一种获取任意预训练回归器不确定性的方法。我们在该框架与贝叶斯推断之间建立了强关联，并开发了一种末层近似方法，使新方法能够应用于神经网络。这一扩展无需对神经网络本身或其训练过程进行任何修改，即可实现低成本的不确定性评估。我们在一系列回归任务中展示了该方法的效果，范围涵盖简单玩具模型直至化学与气象学领域的实际应用。