On Objective Function, Regularizer, and Prediction Error of a Learning Algorithm for Dealing With Multiplicative Weight Noise

In this paper, an objective function for training a functional link network to tolerate multiplicative weight noise is presented. Basically, the objective function is similar in form to other regularizer-based functions that consist of a mean square training error term and a regularizer term. Our study shows that under some mild conditions the derived regularizer is essentially the same as a weight decay regularizer. This explains why applying weight decay can also improve the fault-tolerant ability of a radial basis function (RBF) with multiplicative weight noise. In accordance with the objective function, a simple learning algorithm for a functional link network with multiplicative weight noise is derived. Finally, the mean prediction error of the trained network is analyzed. Simulated experiments on two artificial data sets and a real-world application are performed to verify theoretical result.