Data envelopment analysis models for probabilistic classification

We propose and test three different probabilistic classification techniques using data envelopment analysis (DEA). The first two techniques assume parametric exponential and half-normal inefficiency probability distributions. The third technique uses a hybrid DEA and probabilistic neural network approach. We test the proposed methods using simulated and real-world datasets. We compare them with cost-sensitive support vector machines and traditional probabilistic classifiers that minimize Bayesian misclassification cost risk. The results of our experiments indicate that the hybrid approach performs as well as or better than other techniques when misclassification costs are asymmetric. The performance of exponential inefficiency distribution DEA classifiers is similar or better than that of traditional probabilistic neural networks. We illustrate that there are certain classification problems where probabilistic DEA based classifiers may provide superior performance compared to competing classification techniques.