Boundary Self-adjusting Prediction Intervals And Its Applications

Compared with the conventional point prediction,Prediction Intervals(PIs)are able to consider the prediction error and output the estimated range of target value,thereby providing more abundant prediction information for subsequent decisionmaking modules.This paper focuses on the topic of neural network-based PIs and explores efficient PIs construction methods.Also,it combines PIs with deep neural networks and stochastic optimization models to solve realistic problems in the areas of autonomous driving and optimized scheduling.Distance-Approaching(DA)Loss is proposed in this paper from the perspective of the distance between the PIs and their target values.The DA loss allows the neural network to be trained by using gradient descent,which leads to the significantly higher training efficiency than the methods based on heuristic search algorithms.The experiments are performed on 9 benchmark datasets and use multi-layer perceptron as the PIs construction model.The results demonstrate that quality of the PIs constructed by DA loss is superior to the other methods,thus the effectiveness of the proposed method is preliminary verified.We propose to solve the trajectory prediction of autonomous driving in the sense of PIs,which is defined as Feasible Region Prediction(FRP)in this work.The DA loss is employed to train the deep neural network,i.e.,the Long Short-Term Memory(LSTM)encoder-decoder.The network will extract the time-series features of historical trajectory and make multi-dimensional,multi-steps prediction for the future feasible region.The experiment results turn out that the DA loss outperforms the other existing method,which proves that the proposed method is able to guide the training process of the deep neural network and make it construct high-quality PIs.In addition,some network architecture design details,which include single/multiple model,the usage of LSTM's coding features and the auxiliary task of trajectory classification,are also discussed and verified experimentally.As for the water-supply scheduling task on seawater desalination system,a “PIs + stochastic scheduling” scheme is proposed.Dependent chance programming model is built and the optimization mechanism by genetic algorithm is introduced.This scheme is especially applicable to the situation where accurate point prediction model is hard to establish due to the data limitation or other reasons.The experiment results show that,compared with the conventional "point prediction + deterministic scheduling" scheme,the proposed scheme can provide a water-supply agenda which is closer to the real demand.Finally,The reason why the “PIs + stochastic scheduling” scheme performs better is explored and the sensitive analysis of the model parameters is presented.