函数型数据支持向量回归

Support vector regression for functional data

函数型数据回归是一个非常有意义的课题.已有工作都是利用平方损失来衡量误差,而本文采用ε-不敏感损失来衡量误差.本文构造基于ε-不敏感损失的逼近元,给出表示形式及其系数计算.逼近元具有鲁棒性和稀疏性等性质.本文的主要结果是,在一些常规条件下建立预测误差收敛阶.与关于平方损失工作相比,我们不要求协方差算子与积分算子之间的"对齐"关系.此外,本文还讨论了支持向量回归函数本身的逼近性质.即使对有限维数据,关于这方面的结果在文献中也尚未见到.

Linear regression for functional data is an important topic. While the existing works are devoted to the regularized least square regression, this paper considers regularized regression with ε-insensitive loss. The approximation element is constructed based on samples and ε-insensitive loss. Under some mild assumptions, we establish a convergence rate as the number of size of samples tends to infinity. Moreover, the approximation of the function itself constructed by support vector regression is discussed. We have not been aware of such result even for finite-dimensional data.