  We propose a simple method that combines neural networks and Gaussian
processes. The proposed method can estimate the uncertainty of outputs and
flexibly adjust target functions where training data exist, which are
advantages of Gaussian processes. The proposed method can also achieve high
generalization performance for unseen input configurations, which is an
advantage of neural networks. With the proposed method, neural networks are
used for the mean functions of Gaussian processes. We present a scalable
stochastic inference procedure, where sparse Gaussian processes are inferred by
stochastic variational inference, and the parameters of neural networks and
kernels are estimated by stochastic gradient descent methods, simultaneously.
We use two real-world spatio-temporal data sets to demonstrate experimentally
that the proposed method achieves better uncertainty estimation and
generalization performance than neural networks and Gaussian processes.
