Abstract This study proposes a novel and efficient dual regression model for possibilistic regression analysis that incorporates the principles of support vector machine (SVM) theory. The dual regression model, which comprises an upper model and a lower model, approximates the observed fuzzy phenomena from the outside and inside directions, respectively, such that the inclusion relationship between those two models holds. The proposed dual regression model better explains the inherent vagueness that exists in a given dataset. It provides the outer and inner bounds for the estimated vagueness region, and allows an estimation of the degree of confidence in the predicted fuzzy output. Using the principles for a twin support vector machine (TSVM), the upper- and lower models are estimated by solving two smaller SVM-type quadratic programming problems (QPPs), instead of a single larger QPP. This strategy significantly increases the learning speed for the proposed algorithm. The structural risk minimization principle of SVM makes the proposed method to yield better generalization ability. The kernel function method offers a model-independent framework for the proposed dual regression model. This paper focuses on the class of radial kernels, which enables the proposed method to conquer the problem of increasing spreads. The radial kernel also gives the proposed method a unified framework that allows both crisp and fuzzy inputs. The experimental results verify the effectiveness and efficiency of the proposed method. In comparison with previous SVM-based dual regression model, the proposed approach significantly improves the sparsity, prediction speed, and training speed.

中文翻译：

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使用支持向量网络的双重可能性回归分析

摘要 本研究为可能性回归分析提出了一种新颖且高效的对偶回归模型，该模型结合了支持向量机 (SVM) 理论的原理。二元回归模型包括上层模型和下层模型，分别从外部和内部两个方向逼近观察到的模糊现象，使得这两个模型之间的包含关系成立。提出的对偶回归模型更好地解释了给定数据集中存在的固有模糊性。它为估计的模糊区域提供了外边界和内边界，并允许对预测模糊输出的置信度进行估计。使用双支持向量机 (TSVM) 的原理，上模型和下模型是通过解决两个较小的 SVM 类型二次规划问题 (QPP) 而不是单个较大的 QPP 来估计的。该策略显着提高了所提出算法的学习速度。SVM 的结构风险最小化原则使得所提出的方法具有更好的泛化能力。核函数方法为提出的对偶回归模型提供了一个独立于模型的框架。本文重点研究径向核的类别，这使所提出的方法能够克服传播增加的问题。径向核还为所提出的方法提供了一个统一的框架，允许清晰和模糊的输入。实验结果验证了所提出方法的有效性和效率。与之前基于 SVM 的对偶回归模型相比，