Bayesian applications of belief networks and multilayer perceptrons for ovarian tumor classification with rejection

Incorporating prior knowledge into black-box classifiers is still much of an open problem. We propose a hybrid Bayesian methodology that consists in encoding prior knowledge in the form of a (Bayesian) belief network and then using this knowledge to estimate an informative prior for a black-box model (e.g. a multilayer perceptron). Two technical approaches are proposed for the transformation of the belief network into an informative prior. The first one consists in generating samples according to the most probable parameterization of the Bayesian belief network and using them as virtual data together with the real data in the Bayesian learning of a multilayer perceptron. The second approach consists in transforming probability distributions over belief network parameters into distributions over multilayer perceptron parameters. The essential attribute of the hybrid methodology is that it combines prior knowledge and statistical data efficiently when prior knowledge is available and the sample is of small or medium size. Additionally, we describe how the Bayesian approach can provide uncertainty information about the predictions (e.g. for classification with rejection). We demonstrate these techniques on the medical task of predicting the malignancy of ovarian masses and summarize the practical advantages of the Bayesian approach. We compare the learning curves for the hybrid methodology with those of several belief networks and multilayer perceptrons. Furthermore, we report the performance of Bayesian belief networks when they are allowed to exclude hard cases based on various measures of prediction uncertainty.