通过惩罚大预测区间宽度,提升不确定性预测的经济性。
Large width penalization for neural network-based prediction interval estimation
- 提出新损失函数,重点惩罚过宽的预测区间。
- 在保持覆盖率的前提下,显著缩小预测区间宽度。
- 适合需控制资源成本的高不确定性场景,如太阳能预测。
在高度不确定环境中,确定性预测仅提供点估计,无法捕捉潜在结果。因此,概率预测因其量化不确定性能力受到关注,其中预测区间(PI)可明确展示置信水平下的上下界。高质量的PI需具备高覆盖率(PICP)和窄宽度。实际应用中,PI宽度常用于风险管理,以准备备用资源。但过宽的区间会增加备份资源成本,尤其在极端情况下决策更关注最坏情况。本文提出一种新PI损失函数,通过加重对大区间宽度的惩罚来减小其平均值。该方法兼容基于梯度的神经网络训练,可集成先进深度学习模型。合成数据实验表明,该方法显著缩小了大区间宽度,同时有效维持所需覆盖率。在太阳辐照度预测中的实际应用验证了其在高不确定性数据中的有效性,并展示了与复杂神经网络模型的良好兼容性。因此,该方法可减少资源过度配置,带来显著成本节约。
原文摘要 · Abstract (English)
Forecasting accuracy in highly uncertain environments is challenging due to the stochastic nature of systems. Deterministic forecasting provides only point estimates and cannot capture potential outcomes. Therefore, probabilistic forecasting has gained significant attention due to its ability to quantify uncertainty, where one of the approaches is to express it as a prediction interval (PI), that explicitly shows upper and lower bounds of predictions associated with a confidence level. High-quality PI is characterized by a high PI coverage probability (PICP) and a narrow PI width. In many real-world applications, the PI width is generally used in risk management to prepare resources that improve reliability and effectively manage uncertainty. A wider PI width results in higher costs for backup resources as decision-making processes often focus on the worst-case scenarios arising with large PI widths under extreme conditions. This study aims to reduce the large PI width from the PI estimation method by proposing a new PI loss function that penalizes the average of the large PI widths more heavily. The proposed formulation is compatible with gradient-based algorithms, the standard approach to training neural networks (NNs), and integrating state-of-the-art NNs and existing deep learning techniques. Experiments with the synthetic dataset reveal that our formulation significantly reduces the large PI width while effectively maintaining the PICP to achieve the desired probability. The practical implementation of our proposed loss function is demonstrated in solar irradiance forecasting, highlighting its effectiveness in minimizing the large PI width in data with high uncertainty and showcasing its compatibility with more complex neural network models. Therefore, reducing large PI widths from our method can lead to significant cost savings by over-allocation of reserve resources.
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