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

Ungar径向基函数（rbf）是一类用于过程控制的人工神经网络。通常，k-Means聚类算法应用于预测器（自变量），之后线性回归层将隐藏单元激活映射到适当的响应（因变量）。pi计划探索适合统计分析的RBF架构。该体系结构的统计模型是一个混合模型，其中混合系数是径向基函数，混合分量是常数或多项式函数。根据用于生成模型的假设，可以得到径向和椭圆基函数的不同推广。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量。此外，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，自动选择基函数的数量，并随着数据的收集而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准确性方面进行比较，并根据需要进行修改，以实现快速、准确和稳健的性能。这是两个研究者的合作项目，一个是数学家，一个是化学工程师，他们来自两个不同的机构。工业数据将由杜邦公司提供。

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.