The relationship between these three performance measures is not well de:ned, but there is a
generally unstated assumption that a classi:er trained to optimize MSE will also tend to optimize
other measures such as A
z and 0:90Az. The validity of that assumption was questioned in recent
studies. In one study, Kupinski et al. compared the performance of neural network models trained in
the conventional manner (i.e., minimize MSE) vs. those trained by a niched Pareto multi-objective
genetic algorithm (NP-GA) which simultaneously maximized sensitivity and speci:city [11]. Using
simulated XOR (exclusive or) data, they found that the ROC curve generated by NP-GA training
was superior to that resulting from conventional training for both a perceptron (logistic discriminant)
and an arti:cial neural network. Kupinski et al. also compared the performance of a conventionally
trained perceptron to a NP-GA trained perceptron for the task of breast mass detection [12]. They
found that while there was no signi:cant diOerence between the models in terms of Az, the NP-GA
trained perceptron was signi:cantly better in terms of the 0:90Az. In other words, the weights identi:ed
by minimizing the MSE were inferior to those identi:ed by the NP-GA in terms of the model’s
performance at high sensitivities.