求解非线性回归问题的Newton算法

A Newton Algorithm for Nonlinear Regression

针对大规模非线性回归问题,提出基于静态储备池的Newton算法.利用储备池搭建高维特征空间,将原始问题转化成与储备池维数相关的线性支持向量回归问题,并应用Newton算法求解.鲁棒损失函数的应用可抑制异常点对预测结果的干扰.通过与SVR(Support Vector Regression)及储备池Tikhonov正则化方法比较,验证了所提方法的快速性、较高的预测精度和较好的鲁棒性.

A Newton algorithm is adopted in static reservoir for large scale nonlinear regression in the paper. Based on high-dimension ＇reservoir＇ state space which translates the nonlinear regression to linear support vector regression（SVR）, the Newton optimization is investigated. Meantime, the robust loss functions are adopted to restrain the interference of outliers. Comparisons with SVR（Support Vector Regression） and ＇reservoir＇ Tikhonov regularization method in experiment, the results demonstrate the proposed algorithm has a fast operation speed, high prediction accuracy and good robustness.