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Sparse Spectrum Warped Input Measures for Nonstationary Kernel Learning
Anthony Tompkins · Rafael Oliveira · Fabio Ramos

Thu Dec 10 09:00 AM -- 11:00 AM (PST) @ Poster Session 5 #1611

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are uniquitous 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.

Author Information

Anthony Tompkins (The University of Sydney)
Rafael Oliveira (The University of Sydney)
Fabio Ramos (University of Sydney, NVIDIA)

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