Enhancing ε-support Vector Regression with Gradient Information
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摘要: 传统的ε-支持向量回归机(ε-support vector regression, ε-SVR)只是根据样本点处的响应值来构建模型, 并没考虑样本点处的梯度信息. 如果样本点处的梯度信息容易获得或者获得的成本并不高, 那就应该将梯度信息应用到模型的构建中. 已有的基于梯度信息的 ε-支持向量回归机模型的构建是从泰勒展开的角度着手, 简单地将梯度信息插入到泰勒展开式中; 本研究另辟蹊径, 并没有去估计样本点邻域内的函数值, 而是将梯度信息作为第二类变量融入到核矩阵中直接构建优化模型, 使模型的构建更为简捷直观, 并据此得到一种新的基于梯度信息的 ε-支持向量回归机(Gradient-enhanced ε-support vector regression, GESVR) 模型. 所提模型通过了常用分析函数及精算领域中的生命表数据的验证, 实验表明, 与传统的 ε-SVR相比, 考虑梯度信息的GESVR模型显著地提高了其预测精度.Abstract: Traditional methods constructing of ε-support vector regression (ε-SVR) do not consider the gradients of the true function but only deal with the exact responses at the samples. If the gradient information is available easily and cheaply, it should be used to enhance the model. The existing research on constructing of ε-SVR with gradient information starts from the perspective of Taylor expansion, and simply inserts the additional objective values in the neighborhood of the sampled points into the corresponding terms of a Taylor expansion. In this paper, the gradient-enhanced ε-support vector regression (GESVR) is developed with a direct formulation by incorporating the gradient information into the kernel matrix. The efficiency of this technique is verified by analytical function fitting and the actuarial data in the life table. The results show that the GESVR provides more reliable prediction results than ε-SVR alone.
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