整体与极端偏差之权衡:一种改进的组合预测优化方法

Trade-off between the global and extreme bias:An improved optimization approach in forecast combination

组合预测是集成学习的重要组成分支,也是提升预测或分类精度的有效手段之一.预测模型的整体偏差度量方法应用成熟广泛,例如在组合预测中,集成模型的样本内均方误差是传统权重优化方法的主要目标损失.然而由于“过拟合”风险的存在,训练误差的最小化并非最小化泛化误差的充分条件.因此为了增加权重优化主体的多样性、减少权重过拟合风险和控制模型尾部损失等,本文定义了用以刻画组合模型极端偏差的度量指标.在此基础上,设计了一种全新的权衡整体和极端偏差的目标损失函数,并构建了基于粒子群优化算法的最优权值求解方法.在黄金和原油价格数据上的仿真实验结果表明,本文所提出的组合预测方法能够有效对抗传统方法的过拟合问题,与简单平均、最优权重法等基准模型相比,能够较好地提升组合预测模型的泛化性能,降低模型预测误差.

Forecast combination is an important branch of ensemble learning and it is also an effective tool to improve the forecasting accuracy.The global bias estimation method of the forecaster has a mature application in various aspects.For instance,ensemble model's insample mean square error is a main objective of traditional weight optimization approaches in forecast combination.However,due to the risk of “overfitting”,the minimization of the training error does not necessarily imply a corresponding minimization of the generalization error.Therefore,to increase diversity of optimization objectives,reduce risk of weight overfitting,and control tail error of ensemble model,this paper defines a metric to capture extreme bias of combined forecaster.Furthermore,a novel objective function is proposed which can make a trade-off between the global and extreme bias to achieve optimal weights.Specifically,the particle swarm optimization method is introduced to achieve the optimal combination weights.The experimental results on gold price and oil price data demonstrate that the proposed forecast combination approach can efficiently reduce overfitting risk and improve the generalization ability,outperforming simple averaging,optimal weight method and other benchmark models.