MULTIVARIATE ADAPTIVE REGRESSION SPLINES
MULTIVARIATE ADAPTIVE REGRESSION SPLINES
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DOI：
10.1214/aos/1176347963
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发表时间：
1991-03-01
影响因子：
4.5
通讯作者：
FRIEDMAN, JH
中科院分区：
文献类型：
--
作者：
FRIEDMAN, JH
提出了一种新的高维数据柔性回归建模方法。该模型采用乘积样条基函数的扩展形式，其中基函数的数量以及与每个基函数相关联的参数（乘积度和节点位置）由数据自动确定。这个过程的动机是递归分区回归方法，并分享其有吸引力的属性。然而，与递归划分不同，这种方法产生具有连续导数的连续模型。它有更多的能力和灵活性来建模几乎是加性的关系或涉及最多几个变量的交互作用。此外，该模型可以以单独识别加性贡献和与不同多变量相互作用相关的加性贡献的形式表示。
A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data. This procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties. Unlike recursive partitioning, however, this method produces continuous models with continuous derivatives. It has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables. In addition, the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions.