  Morden deep ensembles technique achieves strong uncertainty estimation
performance by going through multiple forward passes with different models.
This is at the price of a high storage space and a slow speed in the inference
(test) time. To address this issue, we propose Density-Regression, a method
that leverages the density function in uncertainty estimation and achieves fast
inference by a single forward pass. We prove it is distance aware on the
feature space, which is a necessary condition for a neural network to produce
high-quality uncertainty estimation under distribution shifts. Empirically, we
conduct experiments on regression tasks with the cubic toy dataset, benchmark
UCI, weather forecast with time series, and depth estimation under real-world
shifted applications. We show that Density-Regression has competitive
uncertainty estimation performance under distribution shifts with modern deep
regressors while using a lower model size and a faster inference speed.
