  Recent advances in deep learning have shown that uncertainty estimation is
becoming increasingly important in applications such as medical imaging,
natural language processing, and autonomous systems. However, accurately
quantifying uncertainty remains a challenging problem, especially in regression
tasks where the output space is continuous. 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 Likelihood 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 broad spectrum
of regression problems, including high-dimensional regression.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.
