For regression tasks, standard Gaussian processes (GPs) provide natural uncertainty quantification, while deep neural networks (DNNs) excel at representation learning. We propose to synergistically combine these two approaches in a hybrid method consisting of an ensemble of GPs built on the output of hidden layers of a DNN. GP scalability is achieved via Vecchia approximations that exploit nearest-neighbor conditional independence. The resulting deep Vecchia ensemble not only imbues the DNN with uncertainty quantification but can also provide more accurate and robust predictions. We demonstrate the utility of our model on several datasets and carry out experiments to understand the inner workings of the proposed method.

翻译：对于回归任务，标准高斯过程（GPs）能提供自然的不确定性量化，而深度神经网络（DNNs）则在表示学习方面表现出色。我们提出将这两种方法协同结合，形成一种混合方法：在DNN隐藏层输出基础上构建高斯过程集成。通过利用最近邻条件独立性的Vecchia近似实现GP的可扩展性。由此产生的深度Vecchia集成不仅赋予DNN不确定性量化能力，还能提供更准确且鲁棒的预测。我们在多个数据集上验证了模型的有效性，并通过实验深入探究了所提方法的内在机理。