Filtering Noise in Regression Problems Using a Multiobjective Leaning Algorithm

This paper applies a neural networks (NN) multiobjective learning algorithm called the Minimum Gradient Method (MGM) to filter noise in regression problems. This method is based on the concept that the learning is a bi-objective problem aiming at minimizing the empirical risk (training error) and the function complexity. The complexity is modeled as the norm of the network output gradient. After training, the NN behaves as an adaptive filter which minimizes the cross-validation error. The NN trained with this method can be used to pre-process the data and help reduce the signal-to-noise ratio (SNR). Some results are presented and they show the effectiveness of the proposed approach.