Researchers have proposed several approaches for neural network (NN) based
uncertainty quantification (UQ). However, most of the approaches are developed
considering strong assumptions. Uncertainty quantification algorithms often
perform poorly in an input domain and the reason for poor performance remains
unknown. Therefore, we present a neural network training method that considers
similar samples with sensitivity awareness in this paper. In the proposed NN
training method for UQ, first, we train a shallow NN for the point prediction.
Then, we compute the absolute differences between prediction and targets and
train another NN for predicting those absolute differences or absolute errors.
Domains with high average absolute errors represent a high uncertainty. In the
next step, we select each sample in the training set one by one and compute
both prediction and error sensitivities. Then we select similar samples with
sensitivity consideration and save indexes of similar samples. The ranges of an
input parameter become narrower when the output is highly sensitive to that
parameter. After that, we construct initial uncertainty bounds (UB) by
considering the distribution of sensitivity aware similar samples. Prediction
intervals (PIs) from initial uncertainty bounds are larger and cover more
samples than required. Therefore, we train bound correction NN. As following
all the steps for finding UB for each sample requires a lot of computation and
memory access, we train a UB computation NN. The UB computation NN takes an
input sample and provides an uncertainty bound. The UB computation NN is the
final product of the proposed approach. Scripts of the proposed method are
available in the following GitHub repository: github.com/dipuk0506/UQ

本文提出了一种基于神经网络的不确定性量化方法，该方法考虑灵敏度意识以获取相似样本，通过预测绝对误差来找到不确定性，然后构建初始不确定性界限并进行边界校正，通过 UB 计算 NN 来减少计算和内存访问。