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Support vector interval regression networks for interval regression analysis

机译：支持向量区间回归网络进行区间回归分析

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摘要

In this paper, the support vector interval regression networks (SVIRNs) are proposed for the interval regression analysis. The SVIRNs consist of two radial basis function networks. One network identifies the upper side of data interval, and the other network identifies the lower side of data intervals. Because the support vector regression (SVR) approach is equivalent to solving a linear constrained quadratic programming problem, the number of hidden nodes and the initial values of adjustable parameters can be easily obtained. Since the selection of a parameter ε in the SVR approach may seriously affect the modeling performance, a two-step approach is proposed to properly select the ε value. After the SVR approach with the selected ε, an initial structure of SVIRNs can be obtained. Besides, outliers will not significantly affect the upper and lower bound interval obtained through the proposed two-step approach. Consequently, a traditional back-propagation (BP) learning algorithm can be used to adjust the initial structure networks of SVIRNs under training data sets without or with outliers. Due to the better initial structure of SVIRNs are obtained by the SVR approach, the convergence rate of SVIRNs is faster than the conventional networks with BP learning algorithms or with robust BP learning algorithms for interval regression analysis. Four examples are provided to show the validity and applicability of the proposed SVIRNs.
机译：本文提出了支持向量区间回归网络（SVIRNs）进行区间回归分析。 SVIRN由两个径向基函数网络组成。一个网络标识数据间隔的上侧，另一个网络标识数据间隔的下侧。由于支持向量回归（SVR）方法等效于解决线性约束二次规划问题，因此可以轻松获得隐藏节点的数量和可调参数的初始值。由于在SVR方法中选择参数ε可能会严重影响建模性能，因此建议采用两步法来正确选择ε值。在使用选定的ε的SVR方法之后，可以获得SVIRN的初始结构。此外，离群值不会显着影响通过建议的两步法获得的上下限区间。因此，可以使用传统的反向传播（BP）学习算法在没有或有异常值的训练数据集下调整SVIRN的初始结构网络。由于通过SVR方法可获得更好的SVIRNs初始结构，因此SVIRNs的收敛速度比带有BP学习算法或用于间隔回归分析的强大BP学习算法的常规网络要快。提供了四个示例来说明所提出的SVIRN的有效性和适用性。

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