1 Training Neural Networks Beyond the Euclidean Distance

When committed to forecasting or classification tasks Neural Networks (NNs) are typically trained with respect to Euclidean distance minimisation / likelihood maximisation. This is commonly irrespective of any other end user preferences. In a number of situations, most notably time series forecasting, users may have other objectives than solely Euclidean minimisation. Users may, for example, desire model predictions be consistent in their residual error, be accurate in their directional change predictions, or may prefer other error measures than just Euclidean distance. In this paper a methodology is devised for training Multi Layer Perceptrons (MLPs) with competing error objectives using an Evolutionary Strategy (ES). Experimental evidence is presented, using the Santa Fe competition data, which supports the effectiveness of this training methodology. Identical networks are trained with different and competing error measures. Different solutions are achieved, and these solutions are shown in general to reflect the error measure preferences as defined during training. Areas for future research and model extensions are also discussed.