STATISTICAL MODELS AND NEURAL NETS: BUILDING ON THE STRENGTHS OF BOTH

Artificial Neural Nets (ANN) are a powerful tool in prediction, and, as consequence, in knowledge discovery and data mining. Both mathematical analysis and empirical studies show that a properly trained ANN can produce better prediction than competitors in many circumstances. On the other hand, in spite of a growing interest, ANN still play a limited role in the area of biomedicine, where in general, traditional model building is much more popular. The weakness of ANN is twofold: 1) An ANN is a 'black box', in that it doesn't easily show why the prediction is made; 2) Training an ANN requires a lot of ad hoc manoeuvres that may discourage a non-expert: thus, paradoxically, unimaginative training may produce results which are inferior to simpler but less flexible competitors.

In this seminar an approach will be proposed which integrates statistical models and ANN. The approach is designed with several goals in mind, among these: i) to increase the applicability of the ANN paradigm to more complex data structures; ii) to alleviate the black box aspect of ANN by providing interpretations which are 'close' to statistical models, such as trees or linear/additive models; iii) to provide a systematic approach to training for optimizing prediction.

In particular, the seminar will illustrate the general approach by developing a new training procedure for ANN, based on regularization, cross-validation and initialization by a logistic regression (LR) model. The procedure is expected to produce an ANN predictor at least as good as the LR-based one. Indeed, the procedure was applied to 10 data sets of biomedical interest and ANN and LR were systematically compared. In all data sets, taking deviance as criterion, the ANN predictor outperformed the LR predictor and in 6 cases the improvement was statistically significant. The other evaluation criteria used (C-index, MSE and Error Rate) yielded variable results, but, on the whole, confirmed that proper training may significantly detect improvement of prediction with respect to LR in practical situations of biomedical interest.