Gap-Based Estimation: Choosing the Smoothing Parameters for Probabilistic and General Regression Neural Networks

Probabilistic neural networks (PNN) and general regression neural networks (GRNN) represent the knowledge by a simple but interpretable model that approximates the optimal classifier/predictor in the sense of expected value of accuracy. This model requires an important preset smoothing parameter, which is usually chosen by cross-validation or clustering. In this paper, we demonstrate the difficulties of both these approaches, discuss the relationship between this parameter and some of the data statistics, and attempt to develop a fast approach to determine the optimal value of this parameter. Finally, through experimentation we show that our approach, referred to as a gap-based estimation approach, is superior to the compared approaches.