  Compared to point estimates calculated by standard neural networks, Bayesian
neural networks (BNN) provide probability distributions over the output
predictions and model parameters, i.e., the weights. Training the weight
distribution of a BNN, however, is more involved due to the intractability of
the underlying Bayesian inference problem and thus, requires efficient
approximations. In this paper, we propose a novel approach for BNN learning via
closed-form Bayesian inference. For this purpose, the calculation of the
predictive distribution of the output and the update of the weight distribution
are treated as Bayesian filtering and smoothing problems, where the weights are
modeled as Gaussian random variables. This allows closed-form expressions for
training the network's parameters in a sequential/online fashion without
gradient descent. We demonstrate our method on several UCI datasets and compare
it to the state of the art.
