  Combining Gaussian processes with the expressive power of deep neural
networks is commonly done nowadays through deep kernel learning (DKL).
Unfortunately, due to the kernel optimization process, this often results in
losing their Bayesian benefits. In this study, we present a novel approach for
learning deep kernels by utilizing infinite-width neural networks. We propose
to use the Neural Network Gaussian Process (NNGP) model as a guide to the DKL
model in the optimization process. Our approach harnesses the reliable
uncertainty estimation of the NNGPs to adapt the DKL target confidence when it
encounters novel data points. As a result, we get the best of both worlds, we
leverage the Bayesian behavior of the NNGP, namely its robustness to
overfitting, and accurate uncertainty estimation, while maintaining the
generalization abilities, scalability, and flexibility of deep kernels.
Empirically, we show on multiple benchmark datasets of varying sizes and
dimensionality, that our method is robust to overfitting, has good predictive
performance, and provides reliable uncertainty estimations.
