We propose a simple and efficient approach to generate a prediction intervals (PI) for approximated and forecasted trends. Our method leverages a weighted asymmetric loss function to estimate the lower and upper bounds of the PI, with the weights determined by its coverage probability. We provide a concise mathematical proof of the method, show how it can be extended to derive PIs for parametrised functions and discuss its effectiveness when training deep neural networks. The presented tests of the method on a real-world forecasting task using a neural network-based model show that it can produce reliable PIs in complex machine learning scenarios.

翻译：我们提出了一种简单高效的方法，用于生成近似与预测趋势的预测区间（PI）。该方法利用加权非对称损失函数来估计预测区间的上下界，其中权重由区间的覆盖概率决定。我们提供了该方法的简洁数学证明，阐述了如何将其推广至参数化函数的预测区间推导，并讨论了其在训练深度神经网络时的有效性。通过基于神经网络模型的实际预测任务测试，该方法展现了在复杂机器学习场景中生成可靠预测区间的能力。