Dependence of ATR system performance on size of training sets

Automatic target recognition systems often have parameters that are estimated using training data. These parameters are then used in an implementation of the system as if they are the true parameters. The training sets consist of independent and identically distributed copies of the data given the target type. In an ideal case, we analyze the degradation in performance of such systems as a function of the size of the training sets. The training sets consist of independent and identically distributed copies of the data given the target type. The ideal performance is determined by the true parameters and is characterized in terms of a receiver operating characteristic (ROC) for a two-target problem. For a finite-sized training set the ROC curves fall below the ideal and converge to the ideal as the size of the training sets grows. Since in practical systems we have only a very limited amount of training data, it is desirable to quantify the degradation based on the size of the training sets. This will allow a prediction of the difference between performance obtained empirically and the optimal performance. Laplace approximations for the performance are explored. We study a Gaussian model in detail.