Adaptive multi-resolution Gaussian processes: Scalable exact inference with naturally data-sparse covariance matrices

The paper introduces an adaptive multi‑resolution Gaussian process framework that achieves scalable, exact inference by constructing a naturally data‑sparse covariance matrix using basis functions anchored directly to samples. By shrinking the support domains of these basis functions, the resulting matrix has limited block sizes, ensuring sparsity and enabling efficient computation of its inverse via a sparse Cholesky algorithm. The authors demonstrate that this approach yields exact inference with training cost ≠≠ O(n log^2 n) and prediction cost ≠≠ O(log^d n), while also improving predictive uncertainties through an augmented basis function.

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