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.

通过在测试时间中进行多次前向传递使用不同模型的现代深度集成技术，在不确定性估计方面取得了强大的性能，但代价是高存储空间和较慢的速度。为了解决这个问题，我们提出了一种名为 Density-Regression 的方法，它利用密度函数在不确定性估计中实现了快速推理，并且只需进行一次前向传递。我们证明它在特征空间上与距离相关，这是神经网络在分布转变下产生高质量不确定性估计的必要条件。经验上，我们对立方体玩具数据集、基准 UCI、时间序列天气预测和实际应用中的深度估计进行实验证明，Density-Regression 在分布转变下具有与现代深度回归器相当的不确定性估计性能，同时使用更小的模型尺寸和更快的推理速度。