Statistics and Neural Networks

Feed-forward networks are used to find the best functional fit for a set of input-output examples. Changes to the network weights allow fine-tuning of the network function in order to detect the optimal configuration. However, two complementary motivations determine our perception of what optimal means in this context. On the one hand we expect the network to map the known inputs as exactly as possible to the known outputs. But on the other hand the network must be capable of generalizing, that is, unknown inputs are to be compared to the known ones and the output produced is a kind of interpolation of learned values. However, good generalization and minimal reproduction error of the learned input-output pairs can become contradictory objectives.