Deep kernel processes
This provides a unified probabilistic framework for deep learning models, potentially improving performance in tasks like regression and classification.
The paper introduces deep kernel processes, a framework that transforms Gram matrices using nonlinear kernels and Wishart distributions, and shows that it unifies deep Gaussian processes, Bayesian neural networks, and their infinite variants. It demonstrates that the deep inverse Wishart process outperforms these baselines on standard benchmarks.
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.