基于黄金分割法的加速MARS研究

Fast MARS Based on Golden Section Method

多元自适应回归样条法(Multivariate adaptive regression spline,MARS)是一种专门针对高维数据拟合的回归方法。该方法以样条函数的张量积作为基函数,以样本数据坐标作为可选的节点矢量值,算法过程以失拟度(Lack of fit,LOF)最小为目标优化选择基函数和节点矢量。提出了基于黄金分割的加速MARS算法,引入一维黄金分割搜索算法及计算子区间概念,以提高算法节点矢量和基函数的优化选择效率。最后,四个典型的测试算例验证了所提出的方法在保证模型近似精度的前提下可大幅节省模型构造时间。

Multivariate adaptive regression spline is a regression method with strong ability to generalize specifically for high-dimensional data. MARS uses the tensor product of the splines as basis functions, and takes the sample data coordinate as an optional knot. The process of choosing basis functions and knots targets the minimization of lack-of-fit criterion. An improved algorithm was proposed based on golden section search： The original strategy was replaced by linear golden section search methods, and the concept of calculation intervals was introduced in order to improve the efficiency of the knot and basis function optimization. Several examples were enumerated to illustrate this new method could ensure the model＇s accuracy and save considerable modeling time.