  Classifiers based on neural networks (NN) often lack a measure of uncertainty
in the predicted class. We propose a method to estimate the probability mass
function (PMF) of the different classes, as well as the covariance of the
estimated PMF. First, a local linear approach is used during the training phase
to recursively compute the covariance of the parameters in the NN. Secondly, in
the classification phase another local linear approach is used to propagate the
covariance of the learned NN parameters to the uncertainty in the output of the
last layer of the NN. This allows for an efficient Monte Carlo (MC) approach
for: (i) estimating the PMF; (ii) calculating the covariance of the estimated
PMF; and (iii) proper risk assessment and fusion of multiple classifiers. Two
classical image classification tasks, i.e., MNIST, and CFAR10, are used to
demonstrate the efficiency the proposed method.
