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Gaussian Processes (GPs) are highly expressive, probabilistic models. A majorlimitation is their computational complexity. Naively, exact GP inferencerequires $\mathcal{O}(N^3)$ computations with $N$ denoting the number ofmodeled points. Current approaches to overcome this limitation either rely onsparse, structured or stochastic representations of data or kernel respectivelyand usually involve nested optimizations to evaluate a GP. We present a new,generative method named Iterative Charted Refinement (ICR) to model GPs onnearly arbitrarily spaced points in $\mathcal{O}(N)$ time for decaying kernelswithout nested optimizations. ICR represents long- as well as short-rangecorrelations by combining views of the modeled locations at varying resolutionswith a user-provided coordinate chart. In our experiment with points whosespacings vary over two orders of magnitude, ICR's accuracy is comparable tostate-of-the-art GP methods. ICR outperforms existing methods in terms ofcomputational speed by one order of magnitude on the CPU and GPU and hasalready been successfully applied to model a GP with $122$ billion parameters.

Sparse Kernel Gaussian Processes through Iterative Charted Refinement (ICR)