基于核密度估计的鲁棒随机结构网络
Robust Stochastic Configuration Networks with Kernel Density Estimation
摘要：
神经网络已被广泛用作拟合数据分布的预测模型，并且它们可以通过学习样本集合来实现。然而，在许多应用中，给定的数据集可能包含噪声样本或离群值，这可能导致在泛化方面较差的学习器模型。本文致力于发展鲁棒随机配置网络（RSCN）解决不确定数据回归问题。RSCN建立在原始随机配置网络的基础上，采用加权最小二乘法确定输出权值，输入权值和偏差通过满足一组不等式约束递增随机生成。采用核密度估计（kerneldensityestimation，KDE）方法为每个训练样本设置惩罚权值，以减少噪声数据或离群值对学习模型的负面影响。交替优化技术应用于更新RSCN模型与改进的惩罚权计算从核密度估计函数。通过一个函数逼近、四个基准数据集和一个工程应用实例对算法进行了性能评估。其他强大的随机神经建模技术，包括概率鲁棒学习算法的神经网络与随机权重和改进的RVFL网络的比较表明，建议RSCN与KDE表现良好，并表现出良好的潜力，为现实世界的应用。
英文摘要：
Neural networks have been widely used as predictive models to fit data distribution, and they could be implemented through learning a collection of samples. In many applications, however, the given dataset may contain noisy samples or outliers which may result in a poor learner model in terms of generalization. This paper contributes to a development of robust stochastic configuration networks (RSCNs) for resolving uncertain data regression problems. RSCNs are built on original stochastic configuration networks with weighted least squares method for evaluating the output weights, and the input weights and biases are incrementally and randomly generated by satisfying with a set of inequality constrains. The kernel density estimation (KDE) method is employed to set the penalty weights for each training samples, so that some negative impacts, caused by noisy data or outliers, on the resulting learner model can be reduced. The alternating optimization technique is applied for updating a RSCN model with improved penalty weights computed from the kernel density estimation function. Performance evaluation is carried out by a function approximation, four benchmark datasets and a case study on engineering application. Comparisons to other robust randomised neural modelling techniques, including the probabilistic robust learning algorithm for neural networks with random weights and improved RVFL networks, indicate that the proposed RSCNs with KDE perform favourably and demonstrate good potential for real-world applications.
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