Abstract:

An asymmetric [ν]- kernel-free quadratic surface support vector regression is proposed. By introducing the Pinball loss function, the training points above and below the[ε]band are given different penalties, so the better regression function is obtained. Furthermore, the parameters [p] and[ν]control the upper bound of the number of the training points classified incorrectly above and below the[ε]band. When [p=0.5], the method is degenerated into a symmetric [ν]-kernel-free quadratic surface support vector regression, and the number of support vectors which can be controlled by parameter[ν]is also proved. In fact, the algorithm is kernel free, thus avoiding the selection of kernel parameter without losing the interpretability of the decision function. The numerical experiment shows that the proposed approach has better fitting performance and less time consumption, and the parameter [p] will not increase the computational burden.

Key words: [ν]-support vector regression, kernel-free quadratic surface support vector regression, Pinball loss

摘要：

针对回归问题提出了非对称[ν]-无核二次曲面支持向量回归机。通过引入Pinball损失函数，使得位于[ε]带上方和下方的样本点具有不同的惩罚，从而得到更优的回归函数。进一步从理论上分析了参数[p]和[ν]控制[ε]带上方和下方错误样本点数目的上界。当[p=0.5]时，该方法就退化成了对称[ν]-无核二次曲面支持向量回归机，此时也证明了参数[ν]可控制支持向量的个数。事实上，该算法不需要使用核函数，从而避免了核参数的选择且不损失决策函数的可解释性。数值实验部分展示了该算法具有更好的拟合性能且耗时较少，也分析了参数[p]不会增加计算成本。

关键词: [&nu, ]-支持向量回归机, 无核二次曲面支持向量回归机, Pinball损失