基于GWO优化的L1正则化分数阶灰色时间幂预测模型

L1 Regularized Fractional Grey Time Power Forecasting Model Based on GWO Optimization

灰色预测模型是一类处理小样本数据预测的有效方法,其中单变量灰色预测模型GM(1,1,tα)是一个重要的研究对象。FAGM(1,1,tα)模型是在基于一阶累加的GM(1,1,tα)模型的基础上引入分数阶累加形式的预测模型。然而,该模型的精度不够高,且容易存在过拟合现象。本文结合Lasso回归中的L1正则化思想,对分数阶累加的灰色时间幂模型FAGM(1,1,tα)进行正则化,提出正则化分数阶灰色时间幂预测模型LFAGM(1,1,tα),使用坐标下降算法替代最小二乘估计来求解模型的参数。同时,使用灰狼优化算法(GWO)搜索LFAGM(1,1,tα)模型的最优非线性参数。并基于中国农业耕地灌溉面积情况(2008~2019年)进行算例分析,结果表明,LFAGM(1,1,tα)模型具有更高的预测精度。

Grey prediction model is an effective method for dealing with small sample data prediction, in which univariate grey prediction model GM(1,1,tα) is an important research object. The FAGM(1,1,tα) model is a prediction model based on the first-order cumulative GM(1,1,tα) model by introducing the fractional-order cumulative form. However, the accuracy of the model is not high enough and it is prone to over-fitting. This paper combines the L1 regularization idea in Lasso regression to regularize the fractional cumulative gray time power model FAGM(1,1,tα), and proposes a regularized fractional gray time power prediction model LFAGM(1,1,tα), using co- ordinate descent algorithm instead of least squares estimation to solve the model parameter. At the same time, Grey Wolf Optimization (GWO) is used to search the optimal nonlinear parameters of LFAGM(1,1,tα) model. Based on the agricultural farmland irrigation area in China (2008~ 2019), the results show that the LFAGM(1,1,tα) model has higher prediction accuracy.