Studies of model selection and regularization for generalization in neural networks with applications

This thesis investigates the generalization problem in artificial neural networks, attacking it from two major approaches: regularization and model selection. On the regularization side, under the framework of Kullback-Leibler divergence for feedforward neural networks, we develop a new formula for the regularization parameter in Gaussian density kernel estimation based on available training data sets. Experiments show that the estimated regularization parameter is valid for most cases. With the derived formula, all sample data sets can be used to estimate the smoothing parameter, which is less computationally expensive than using the leave-one-out cross-validation method. Furthermore, the new covariance matrix estimation formula is suitable for small sample data with high dimension setting in the regularized Gaussian classifier case. On the model selection side, both theory and extensive experiments are conducted for investigating the Bayesian Ying-Yang (BYY) model selection criterion to determine the cluster number in small sample-size cases. We derive new formula for estimating the smoothing parameters with proper approximations in the Smoothed Expectation-Maximum (SEM) technique. Experimental results show that with improved mixture model parameters, the BYY model selection criterion performance is enhanced. From the model selection viewpoint, generalization can also be improved by combining several nets to form ensemble networks. The relationship between Mixture of Experts (ME) and the ensemble networks is established in this thesis. In an approximation where ME reduces to ensemble neural nets, the ensemble nets can be globally optimized instead of being individual members. A new method is consequently proposed to average ensemble networks in the parameter space. The stacked generalization method provides a way of combining trained networks altogether. This approach uses partitioning of the data set to find an overall system which improves generalization performance. In order to investigate this scheme effectively, we develop a new learning algorithm called Pseudoinverse Learning algorithm (PIL). The efficiency of the PIL algorithm is demonstrated through several experiments. Two applications are investigated in detail for model selection. The first application is in the image processing area. Automatic determination of the region number in image segmentation is a step to high level understanding and interpretation of an image by machine. A model selection criterion can be applied to determine the region number if the number of segments to be yielded is equal to the number of clusters in the image feature space. Experimental results show that with the model selection criterion, we can determine a reasonable region number for automatic image segmentation without a priori knowledge. Another application is in the software reliability modeling area. We investigate the use of the mixture model analysis as a tool for early prediction of fault-prone program modules. The EM algorithm is engaged to build the model. By employing only software size and complexity metrics, this technique facilitates the development of an unsupervised model for predicting software quality without the prior knowledge of the number of faults in the modules. The technique is successful in classifying software into fault-prone and non fault-prone modules with a relatively low error rate, thus providing a reliable indicator for software quality prediction.