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Gaussian processes are powerful models for probabilistic machine learning,but are limited in application by their $O(N^3)$ inference complexity. Wepropose a method for deriving parametric families of kernel functions withcompact spatial support, which yield naturally sparse kernel matrices andenable fast Gaussian process inference via sparse linear algebra. Thesefamilies generalize known compactly-supported kernel functions, such as theWendland polynomials. The parameters of this family of kernels can be learnedfrom data using maximum likelihood estimation. Alternatively, we can quicklycompute compact approximations of a target kernel using convex optimization. Wedemonstrate that these approximations incur minimal error over the exact modelswhen modeling data drawn directly from a target GP, and can out-perform thetraditional GP kernels on real-world signal reconstruction tasks, whileexhibiting sub-quadratic inference complexity.

Sparse Gaussian Processes via Parametric Families of Compactly-supported Kernels