Bayesian deep learning approaches that allow uncertainty estimation for regression problems often converge slowly and yield poorly calibrated uncertainty estimates that can not be effectively used for quantification. Recently proposed post hoc calibration techniques are seldom applicable to regression problems and often add overhead to an already slow model training phase. This work presents a fast calibrated uncertainty estimation method for regression tasks, called posterior annealing, that consistently improves the convergence of deep regression models and yields calibrated uncertainty without any post hoc calibration phase. Unlike previous methods for calibrated uncertainty in regression that focus only on low-dimensional regression problems, our method works well on a wide spectrum of regression problems. Our empirical analysis shows that our approach is generalizable to various network architectures including, multilayer perceptrons, 1D/2D convolutional networks, and graph neural networks, on five vastly diverse tasks, i.e., chaotic particle trajectory denoising, physical property prediction of molecules using 3D atomistic representation, natural image super-resolution, and medical image translation using MRI images.

翻译：贝叶斯深度学习在回归问题中的不确定性估计方法通常收敛缓慢，且生成的校准不确定性估计无法有效用于量化。近期提出的后验校准技术很少适用于回归问题，且往往给已缓慢的模型训练阶段增加额外负担。本文提出一种用于回归任务的快速校准不确定性估计方法——后验退火，该方法能持续提升深度回归模型的收敛速度，无需后验校准阶段即可生成校准的不确定性估计。与以往仅聚焦低维回归问题的校准不确定性方法不同，我们的方法在广泛的回归问题中均表现优异。实验分析表明，该方法可泛化至多种网络架构（包括多层感知机、一维/二维卷积网络和图神经网络），并在五个差异显著的任务（混沌粒子轨迹去噪、基于三维原子表征的分子物性预测、自然图像超分辨率及基于磁共振图像的医学图像翻译）上取得良好效果。