We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian measures on the Hilbert space of square-integrable functions in order to determine a variational posterior using a tractable optimisation criterion and avoids pathologies arising in standard variational function space inference. An exciting application of GWI is the ability to use deep neural networks in the variational parametrisation of GWI, combining their superior predictive performance with the principled uncertainty quantification analogous to that of Gaussian processes. The proposed method obtains state-of-the-art performance on several benchmark datasets.

翻译：我们为无限功能空间的普遍变异推断制定了框架,并用这一框架构建了一种称为高斯瓦西斯坦推理法(GWI)的方法。GWI利用高斯泰在高斯泰关于可立体功能的Hilbert空间测量法之间的瓦西斯坦距离,以便使用可移动优化标准确定变异后部,避免标准变异功能空间推理中出现病理。GWI的一个令人振奋的应用是在GWI的变异平衡中利用深神经网络的能力,将高超预测性能与与类似于Gaussian进程的原则不确定性量化方法相结合。拟议方法在若干基准数据集中获得了最新的最新表现。