Obtaining heteroscedastic predictive uncertainties from a Bayesian Neural Network (BNN) is vital to many applications. Often, heteroscedastic aleatoric uncertainties are learned as outputs of the BNN in addition to the predictive means, however doing so may necessitate adding more learnable parameters to the network. In this work, we demonstrate that both the heteroscedastic aleatoric and epistemic variance can be embedded into the variances of learned BNN parameters, improving predictive performance for lightweight networks. By complementing this approach with a moment propagation approach to inference, we introduce a relatively simple framework for sampling-free variational inference suitable for lightweight BNNs.

翻译：从贝叶斯神经网络（BNN）中获取异方差预测不确定性对诸多应用至关重要。通常，除预测均值外，异方差偶然不确定性被作为BNN的额外输出进行学习，然而这种做法可能需向网络中添加更多可学习参数。本研究证明，异方差偶然不确定性与认知方差均可嵌入至学习到的BNN参数方差中，从而提升轻量级网络的预测性能。通过将这一方法与基于矩传播的推断策略相结合，我们提出了一种相对简洁的免采样变分推断框架，适用于轻量级BNN。