Improving biosignal processing through modeling uncertainty: Bayes vs. non-bayes in sleep staging

In this paper we report about an investigation of Bayesian inference applied to neural networks multilayer perceptrons (MLP), in particular in the task of automatic sleep staging based on electroencephalogram (EEG) and electrooculogram (EOG) signals. The main focus was on evaluating the use of so-called "doubt-levels" and "confidence intervals" ("error bars") in improving the results by rejecting uncertain cases and patterns not well represented by the training set. Bayesian inference is used to arrive at distributions of network weights based on training data. We compare the results of the full-blown Bayesian method with results obtained from a k-nearest neighbor classifier. The results show that the Bayesian technique significantly outperforms the k-nearest-neighbor classifier. At the same time, we show that Bayesian inference, for which we have developed an extension for the calculation of error bars in the latent space of hidden units, can indeed be used for improving results by rejecting cases below a doubt-level threshold of probability, as well as for the rejection of artifacts. The performance of the Bayesian solution, however, is not significantly better than alternative techniques such as doubt levels applied to a maximum posterior approach, or the use of density estimation for outlier rejection. We conclude that Bayesian inference is a valid and valuable technique for model estimation but in the given application does not lead to improved results over simpler techniques.