A METHOD OF GENERATING OBJECTIVE FUNCTIONS FOR PROBABILITY ESTIMATION

Multi-Layer Neural Networks (MLNNs) have been known to be used to mode l the statistical properties of their training data. Several authors h ave shown that, depending on the objective function chosen, MLNNs esti mate the posterior class probabilities of their inputs, provided the n etwork is trained with binary desired outputs. If has recently been sh own that conditions exist that define a general class of objective fun ctions which provide probability estimates. This paper introduces a me thod of generating such objective functions. This generator is simple to use, and so far has been found to be universally applicable. Known objective functions, which include the mean-squared error (MSE) and th e cross entropy (CE) measure, are generated here as examples of its ap plication. To demonstrate the potential of this method a new objective function is derived and discussed. This work provides practising engi neers with an explicit method for generating objective functions that could be used in their classification applications. Copyright (C) 1996 Elsevier Science Ltd