We explore the link between deep ensembles and Gaussian processes (GPs) through the lens of the Neural Tangent Kernel (NTK): a recent development in understanding the training dynamics of wide neural networks (NNs). Previous work has shown that even in the infinite width limit, when NNs become GPs, there is no GP posterior interpretation to a deep ensemble trained with squared error loss. We introduce a simple modification to standard deep ensembles training, through addition of a computationally-tractable, randomised and untrainable function to each ensemble member, that enables a posterior interpretation in the infinite width limit. When ensembled together, our trained NNs give an approximation to a posterior predictive distribution, and we prove that our Bayesian deep ensembles make more conservative predictions than standard deep ensembles in the infinite width limit. Finally, using finite width NNs we demonstrate that our Bayesian deep ensembles faithfully emulate the analytic posterior predictive when available, and can outperform standard deep ensembles in various out-of-distribution settings, for both regression and classification tasks.

我们通过神经切向核（NTK）探索深度集合和高斯过程（GPs）之间的联系，引入对标准深度集合训练的简单修改，其中包括对每个群集成员的可计算、随机且不可训练的函数的添加，以在无限宽度下启用后验解释，用于回归和分类任务中，证明了我们的贝叶斯深度集成在无限宽度限制下进行更保守的预测，可在不同的寻常数据的情况下胜过标准的深度集成。

神经切向核下的贝叶斯深度集成