区间因变量不精确回归的神经网络模型
Neural network model for imprecise regression with interval dependent variables
摘要：
本文提出了一种计算上可行的方法来计算严格的区间广义回归分析的输出变量的认知不确定性的界限。新的迭代方法使用机器学习算法将不精确的回归模型拟合到由区间而不是点值组成的数据。该方法是基于一个单层的区间神经网络，可以训练产生的区间预测。它寻求最佳模型的参数，最大限度地减少因变量的实际和预测区间值之间的均方误差，使用一阶基于梯度的优化和区间分析计算来模拟数据的测量不精确性。多层神经网络的一个额外的扩展。我们认为解释变量是精确的点值，但测量的相关值的特征在于区间界限没有任何概率信息。所提出的迭代方法估计的期望区域，这是一个信封的所有可能的精确回归线获得的普通回归分析的基础上的任何配置的实值点从各自的y-区间和它们的x-值的下限和上限。
英文摘要：
This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine learning algorithms to fit an imprecise regression model to data that consist of intervals rather than point values. The method is based on a single-layer interval neural network which can be trained to produce an interval prediction. It seeks parameters for the optimal model that minimizes the mean squared error between the actual and predicted interval values of the dependent variable using a first-order gradient-based optimization and interval analysis computations to model the measurement imprecision of the data. An additional extension to a multi-layer neural network is also presented. We consider the explanatory variables to be precise point values, but the measured dependent values are characterized by interval bounds without any probabilistic information. The proposed iterative method estimates the lower and upper bounds of the expectation region, which is an envelope of all possible precise regression lines obtained by ordinary regression analysis based on any configuration of real-valued points from the respective y-intervals and their x-values.
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