正则化和交叉验证在组合预测模型中的应用

组合预测模型的权重确定方式对于提高模型精度至关重要，为研究正则化与交叉验证是否能改善组合预测模型的预测效果，提出将正则化和交叉验证应用于基于最小二乘法的组合预测模型.通过在组合模型的最优化求解中分别加入L₁、L₂范数正则化项，并对数据集进行留一交叉验证后发现：L₁、L₂范数正则化都对组合模型的预测精度具有改善效果，且L₁范数正则化比L₂范数正则化对组合预测模型的改善效果更好，并且参与组合预测的单项预测模型越多，正则化的改善效果越好，交叉验证对组合预测模型的改善效果则与给定实验数据量呈现正相关.

Application of Regularization and Cross-Validation in Combination Forecasting Model

To determine the weight of the combined forecasting model is very important to improve the accuracy of the model. Applying the regularization and cross-validation to the combined forecasting model based on the least squares method is for studying whether the regularization and cross-validation can improve the prediction effect of the combined forecasting model. It is carried out by adding the L₁ and L₂ norm regularization terms to the optimization solution of the combined model and using leave-one-out-cross-validation in the data set. The result shows that both the L₁ and L₂ norm regularization can improve prediction accuracy of the combined model to a certain degree. Moreover, the L₁ norm regularization is better than the L₂ norm regularization for the combined forecasting model, and the more single forecasting models participating in the combined forecasting, the better the regularization improvement effect. In addition, there is a positive correlation between the cross-validation improvement effect and amount of experimental data given.