Bayesian Neural Network with and without compensation for competing risks

This paper addresses the problem of compensation mechanisms which can be used by Bayesian Neural Networks (BNNs) when dealing with skewed training data. The compensation mechanisms are used to balance the training data towards a mean value so that to be able to calculate the marginalized neural network predictions. There are presented 2 compensation mechanisms and each of them is applied to a BNN: a local compensation mechanism and a global mechanism. There is presented a third BNN model which does not use a compensation mechanism. It is shown that in the absence of a compensation mechanism, the marginalized network outputs can still be calculated through a scaling of the Jacobian and Hessian matrixes involved in the respective calculations. The standard BNN is a Partial Logistic Artificial Neural Network with Automatic Relevance Determination, which has multiple competing network outputs which corresponds to the Competing Risks (CRs) type of analysis specific to the medical domain of survival analysis. The resulted model is entitled the PLANN-CR-ARD model. The three versions of the PLANN-CR-ARD model are tested on a very demanding medical dataset taken from the survival analysis. The ARD framework implements the calculation of the network outputs, the marginalization of the network outputs and the model selection. The numerical results show that the neural network model based on the global compensation is very effective.