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Interval regression analysis using support vector networks

机译：使用支持向量网络的区间回归分析

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摘要

Support vector machines (SVMs) have been very successful in pattern classification and function estimation problems for crisp data. In this paper, the v-support vector interval regression network (v-SVIRN) is proposed to evaluate interval linear and nonlinear regression models for crisp input and output data. As it is difficult to select an appropriate value of the insensitive tube width in ε-support vector regression network, the proposed v-SVIRN alleviates this problem by utilizing a new parametric-insensitive loss function. The proposed v-SVIRN automatically adjusts a flexible parametric-insensitive zone of arbitrary shape and minimal size to include the given data. Besides, the proposed method can achieve automatic accuracy control in the interval regression analysis task. For a priori chosen v, at most a fraction v of the data points lie outside the interval model constructed by the proposed v-SVIRN. To be more precise, v is an upper bound on the fraction of training errors and a lower bound on the fraction of support vectors. Hence, the selection of v is more intuitive. Moreover, the proposed algorithm here is a model-free method in the sense that we do not have to assume the underlying model function. Experimental results are then presented which show the proposed v-SVIRN is useful in practice, especially when the noise is heteroscedastic, that is. the noise strongly depends on the input value x.
机译：支持向量机（SVM）在针对清晰数据的模式分类和功能估计问题方面非常成功。在本文中，提出了v支持向量间隔回归网络（v-SVIRN）来评估区间线性和非线性回归模型以获取清晰的输入和输出数据。由于在ε-支持向量回归网络中难以选择不敏感管宽度的适当值，建议的v-SVIRN通过利用新的对参数不敏感的损失函数来缓解此问题。提出的v-SVIRN自动调整任意形状和最小尺寸的灵活参数不敏感区域，以包括给定数据。此外，该方法可以在区间回归分析任务中实现自动精度控制。对于先验选择的v，至多v个数据点位于建议v-SVIRN构建的间隔模型之外。更准确地说，v是训练误差分数的上限，是支持向量分数的下限。因此，v的选择更加直观。此外，在此我们不必假设基础模型功能的意义上，本文提出的算法是一种无模型的方法。然后给出实验结果，表明所提出的v-SVIRN在实践中很有用，特别是当噪声是异方差时。噪声在很大程度上取决于输入值x。

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