In many real-world problems, there is a limited set of training data, but an abundance of unlabeled data. We propose a new method, Generative Posterior Networks (GPNs), that uses unlabeled data to estimate epistemic uncertainty in high-dimensional problems. A GPN is a generative model that, given a prior distribution over functions, approximates the posterior distribution directly by regularizing the network towards samples from the prior. We prove theoretically that our method indeed approximates the Bayesian posterior and show empirically that it improves epistemic uncertainty estimation and scalability over competing methods.

翻译：在许多实际问题中，训练数据有限，但未标记数据却非常丰富。我们提出了一种新方法——生成后验网络（GPNs），该方法利用未标记数据来估计高维问题中的认知不确定性。GPN是一种生成模型，给定函数上的先验分布，它通过将网络向先验样本正则化来直接近似后验分布。我们从理论上证明了该方法确实近似于贝叶斯后验，并在实证中表明，相比于其他方法，它改进了认知不确定性的估计和可扩展性。