We introduce a distance-based neural network model for regression, in which prediction uncertainty is quantified by a belief function on the real line. The model interprets the distances of the input vector to prototypes as pieces of evidence represented by Gaussian random fuzzy numbers (GRFN's) and combined by the generalized product intersection rule, an operator that extends Dempster's rule to random fuzzy sets. The network output is a GRFN that can be summarized by three numbers characterizing the most plausible predicted value, variability around this value, and epistemic uncertainty. Experiments with real datasets demonstrate the very good performance of the method as compared to state-of-the-art evidential and statistical learning algorithms. \keywords{Evidence theory, Dempster-Shafer theory, belief functions, machine learning, random fuzzy sets.
翻译:我们引入了远程神经网络回归模型, 通过真实线上的信念函数对预测不确定性进行量化。 该模型将输入矢量与原型的距离解释为由高森随机模糊数字(GRFN)和通用产品交叉规则(即将Dempster规则延伸至随机模糊装置的操作员)所代表证据的碎片。 网络输出是一个GRFN, 可以用三个数字进行总结, 这三个数字的特征是最可信的预测值、 这一值周围的变异性以及感知性不确定性。 与真实数据集的实验相比,该方法与最新证据和统计学习算法(\ keywords{Evidence理论 {Dempster-Shafer理论 {Evidence 理论 {Dempster-Shafer 理论、 信仰功能、 机器学习、 随机模糊集 。