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.

本文提出了一种通过闭合式贝叶斯推断方法来学习贝叶斯神经网络的新方法，其中将预测分布的计算和权重分布的更新建模为贝叶斯滤波和平滑问题，并通过将权重建模为高斯随机变量的方法，使网络参数的训练具有连续性且无需梯度下降优化方法。该方法在多个 UCI 数据集上进行了演示，并与现有技术进行了比较。