  In this paper, we study random subsampling of Gaussian process regression,
one of the simplest approximation baselines, from a theoretical perspective.
Although subsampling discards a large part of training data, we show provable
guarantees on the accuracy of the predictive mean/variance and its
generalization ability. For analysis, we consider embedding kernel matrices
into graphons, which encapsulate the difference of the sample size and enables
us to evaluate the approximation and generalization errors in a unified manner.
The experimental results show that the subsampling approximation achieves a
better trade-off regarding accuracy and runtime than the Nystr\"{o}m and random
Fourier expansion methods.
