Khosravi Abbas, Nahavandi Saeid, Creighton Doug, Atiya Amir F
Center for Intelligent Systems Research, Deakin University, Geelong, Victoria 3117, Australia.
IEEE Trans Neural Netw. 2011 Mar;22(3):337-46. doi: 10.1109/TNN.2010.2096824. Epub 2010 Dec 23.
Prediction intervals (PIs) have been proposed in the literature to provide more information by quantifying the level of uncertainty associated to the point forecasts. Traditional methods for construction of neural network (NN) based PIs suffer from restrictive assumptions about data distribution and massive computational loads. In this paper, we propose a new, fast, yet reliable method for the construction of PIs for NN predictions. The proposed lower upper bound estimation (LUBE) method constructs an NN with two outputs for estimating the prediction interval bounds. NN training is achieved through the minimization of a proposed PI-based objective function, which covers both interval width and coverage probability. The method does not require any information about the upper and lower bounds of PIs for training the NN. The simulated annealing method is applied for minimization of the cost function and adjustment of NN parameters. The demonstrated results for 10 benchmark regression case studies clearly show the LUBE method to be capable of generating high-quality PIs in a short time. Also, the quantitative comparison with three traditional techniques for prediction interval construction reveals that the LUBE method is simpler, faster, and more reliable.
文献中已提出预测区间（PIs），通过量化与点预测相关的不确定性水平来提供更多信息。基于神经网络（NN）构建预测区间的传统方法存在对数据分布的限制性假设以及大量计算负荷的问题。在本文中，我们提出了一种新的、快速且可靠的方法来构建神经网络预测的预测区间。所提出的上下界估计（LUBE）方法构建一个具有两个输出的神经网络，用于估计预测区间的边界。通过最小化所提出的基于预测区间的目标函数来实现神经网络训练，该目标函数涵盖区间宽度和覆盖概率。该方法在训练神经网络时不需要任何关于预测区间上下界的信息。应用模拟退火方法来最小化成本函数并调整神经网络参数。针对10个基准回归案例研究的展示结果清楚地表明，LUBE方法能够在短时间内生成高质量的预测区间。此外，与三种构建预测区间的传统技术的定量比较表明，LUBE方法更简单、更快且更可靠。
