r-SVR中参数r与输入噪声间线性反比关系的仿真研究

Experimental Studies on Inversely Linear Dependency between r and the Input Noise in r-support Vector Regression

为研究r范数-支持向量回归机,r-SVR的鲁棒性,验证r-SVR中参数r与输入噪声方差之间的近似反比线性关系,对r-SVR进行了仿真。推导出了作为仿真的依据的 r-SVR的解的形式和对其进行求解的牛顿迭代公式。仿真结果显示:输入噪声为高斯分布时,r-SVR中参数r与输入噪声方差之间存在近似线性反比关系;这一关系曲线随着信噪比增加而斜率减小、整个曲线下移。这一结果印证和丰富了现前的理论推导结果,为在已知输入高斯噪声方差时合理地选择r提供了更可信的依据。

When the distribution of the input noise is known, the optimal parameter choice for the loss function can help SVR enhance its robustness. R-loss function is a more general form of both quadratic loss function and Laplacian loss function. Therefore, research on the dependency relationship between parameter r in r-loss function and input noise has more general significance. It has been theoretically deduced that inversely linear dependency exists between r and the input noise in r-SVR. In this paper, we intend to validate the linear dependency between r and the input noise through studying its implementation method and simulations. We derive the solution of r-SVR by using the Newton descent method. Our experimental results confirm the previously obtained theoretical conclusion.