Maximum Likelihood Estimation of Radial Basis Function Neural Networks for Process Control

径向基函数(RBF)是一类应用于过程控制的人工神经网络。通常，k-均值聚类算法被应用于预测器(自变量)，之后线性回归层将隐藏单元的激活映射到适当的响应(因变量)。私人投资机构计划探索一种适用于统计分析的径向基函数架构。该体系结构背后的统计模型是混合模型，其中混合系数是径向基函数，混合分量是常量或多项式函数。根据用于生成模型的假设，会产生不同的径向基函数和椭圆基函数。这允许使用期望最大化(EM)技术来寻找参数的最大似然估计器。此外，还将开发算法来部分反转网络，估计网络的局部预测误差，识别新的数据点，自动选择基函数，并在收集数据时有效地增量更新网络。这些技术将在化工厂的真实数据上进行测试，与其他近似方法在速度和精度方面进行比较，并根据需要进行修改，以实现快速、准确和稳健的性能。这是两个不同机构的两名研究人员--一名数学家和一名化学工程师--之间的协调项目。工业数据由杜邦公司提供。

Abstract - Ungar Radial Basis Functions (RBFs) are a class of artificial neural networks for process control applications. Commonly, the k-Means clustering algorithm is applied to the predictor ( independent variables), after which a linear regression layer maps the hidden unit activations to the appropriate responses (dependent variables). The PIs plan to explore an RBF architecture which is suited to statistical analysis. The statistical model underlying the architecture is a mixture model in which the mixture coefficients are radial basis functions and the mixture components are constant or polynomial functions. Depending on the assumptions used to generate the model, different generalizations of radial and elliptical basis functions result. This allows the use of the expectation maximization (EM) technique for finding maximum likelihood estimators of the parameters. In addition, algorithms will be developed to partially invert the networks, estimate the local prediction error of the network, recognize novel data points, automatically select the number of basis functions, and incrementally update the network efficiently as data are collected. The techniques will be tested on real data from chemical plants, compared to other approximation methods with respect to speed and accuracy, and modified as needed to achieve fast, accurate, and robust performance. This is a coordinated project between two investigators, a mathematician and a chemical engineer, at two different institutions. Industrial data are to be provided by the DuPont Company.