We define deep kernel processes in which positive definite Gram matrices are progressively transformed by nonlinear kernel functions and by sampling from (inverse) Wishart distributions. Remarkably, we find that deep Gaussian processes (DGPs), Bayesian neural networks (BNNs), infinite BNNs, and infinite BNNs with bottlenecks can all be written as deep kernel processes. For DGPs the equivalence arises because the Gram matrix formed by the inner product of features is Wishart distributed, and as we show, standard isotropic kernels can be written entirely in terms of this Gram matrix -- we do not need knowledge of the underlying features. We define a tractable deep kernel process, the deep inverse Wishart process, and give a doubly-stochastic inducing-point variational inference scheme that operates on the Gram matrices, not on the features, as in DGPs. We show that the deep inverse Wishart process gives superior performance to DGPs and infinite BNNs on standard fully-connected baselines.

本文介绍了深度核过程的概念，探究了深度高斯过程、贝叶斯神经网络以及无限贝叶斯神经网络等模型与深度核过程的等价性，并提出了便于求解的深度逆 Wishart 过程，并通过 Gram 矩阵进行了基于感应点的变分推断，取得了优于标准全连接基线的性能表现。

深核过程