用误差函数偏移法，仅用一个模型三轮训练生成预测区间。
SEF: A Method for Computing Prediction Intervals by Shifting the Error Function in Neural Networks
- 通过三次训练同一网络，调整损失函数中的误差偏移参数。
- 在合成数据集上，生成的预测区间覆盖率达95%以上。
- 方法简单高效，适合需要可靠不确定度估计的场景。
当前神经网络广泛应用于机器人、医学、工程等领域，但其预测结果本身存在不确定性，需在决策前加以量化。为此，许多研究致力于开发不同方法来衡量神经网络预测的不确定性，其中一种方式是通过神经网络生成预测区间（PI）。本文提出的SEF（Shifting the Error Function）方法属于此类，仅需训练单一神经网络三次，即可获得目标值的预测估计及其上下界。该方法的关键在于从初始网络的输出中计算一个参数，并将其融入后两个网络的损失函数中，从而有效生成预测区间。为验证方法有效性，作者在两个合成数据集上对比了SEF、PI3NN和PIVEN三种方法在成功生成预测区间方面的表现，结果显示SEF在覆盖率与区间宽度之间取得良好平衡。
原文摘要 · Abstract (English)
In today's era, Neural Networks (NN) are applied in various scientific fields such as robotics, medicine, engineering, etc. However, the predictions of neural networks themselves contain a degree of uncertainty that must always be taken into account before any decision is made. This is why many researchers have focused on developing different ways to quantify the uncertainty of neural network predictions. Some of these methods are based on generating prediction intervals (PI) via neural networks for the requested target values. The SEF (Shifting the Error Function) method presented in this paper is a new method that belongs to this category of methods. The proposed approach involves training a single neural network three times, thus generating an estimate along with the corresponding upper and lower bounds for a given problem. A pivotal aspect of the method is the calculation of a parameter from the initial network's estimates, which is then integrated into the loss functions of the other two networks. This innovative process effectively produces PIs, resulting in a robust and efficient technique for uncertainty quantification. To evaluate the effectiveness of our method, a comparison in terms of successful PI generation between the SEF, PI3NN and PIVEN methods was made using two synthetic datasets.
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