论文标题
深内核过程
Deep kernel processes
论文作者
论文摘要
我们定义了深内核过程，其中积极确定的革兰氏矩阵会通过非线性核函数逐渐转换，并通过（反向）WishArt分布进行采样。值得注意的是，我们发现深层过程（DGP），贝叶斯神经网络（BNN），无限的BNN和带有瓶颈的无限BNN都可以写入深核过程。对于dgps而言，出现等效性是因为特征的内部产物是wishArt分布式的，并且正如我们所显示的，标准的各向同性核可以完全用这个革兰氏矩阵编写 - 我们不需要对基础特征的了解。我们定义了一个可拖动的深内核过程，深层的欲望值过程，并给出了双重诱导的诱导点变异推理方案，该方案在革兰氏矩阵上工作，而不是在特征上，如DGP中。我们表明，深层的欲望工艺为标准完全连接的基准的DGP和无限BNN提供了出色的性能。
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.
