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：在许多实际应用中，从贝叶斯神经网络（BNN）获取异方差预测不确定性至关重要。通常，异方差偶然不确定性会作为预测均值之外的BNN输出进行学习，但这种方法可能需要在网络中增加更多可学习参数。本研究表明，异方差偶然方差和认知方差均可嵌入到所学BNN参数的方差中，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方法相结合，我们提出了一种相对简单的框架，适用于无需采样的轻量级BNN变分推断。