  We establish a general form of explicit, input-dependent, measure-valued
warpings for learning nonstationary kernels. While stationary kernels are
ubiquitous and simple to use, they struggle to adapt to functions that vary in
smoothness with respect to the input. The proposed learning algorithm warps
inputs as conditional Gaussian measures that control the smoothness of a
standard stationary kernel. This construction allows us to capture
non-stationary patterns in the data and provides intuitive inductive bias. The
resulting method is based on sparse spectrum Gaussian processes, enabling
closed-form solutions, and is extensible to a stacked construction to capture
more complex patterns. The method is extensively validated alongside related
algorithms on synthetic and real world datasets. We demonstrate a remarkable
efficiency in the number of parameters of the warping functions in learning
problems with both small and large data regimes.
