On the Capability of Neural Networks to Approximate the Neyman-Pearson Detector: A Theoretical Study

In this paper, the application of neural networks for approximating the Neyman-Pearson detector is considered. We propose a strategy to identify the training parameters that can be controlled for reducing the effect of approximation errors over the performance of the neural network based detector. The function approximated by a neural network trained using the mean squared-error criterion is deduced, without imposing any restriction on the prior probabilities of the clases and on the desired outputs selected for training, proving that these parameters play an important role in controlling the sensibility of the neural network detector performance to approximation errors. Another important parameter is the signal-to-noise ratio selected for training. The proposed strategy allows to determine its best value, when the statistical properties of the feature vectors are known. As an example, the detection of gaussian signals in gaussian interference is considered.