Sparse Spectrum Warped Input Measures for Nonstationary Kernel Learning
This provides a more efficient method for nonstationary kernel learning in machine learning applications with varying smoothness patterns.
The paper tackles the problem of learning nonstationary kernels for functions with varying smoothness by proposing input-dependent measure-valued warpings that transform stationary kernels, achieving remarkable parameter efficiency in both small and large data regimes.
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.