Fast spatial Gaussian process maximum likelihood estimation via skeletonization factorizations

Abstract

Maximum likelihood estimation for parameter-fitting given observations from a Gaussian process in space is a computationally-demanding task that restricts the use of such methods to moderately-sized datasets. We present a framework for unstructured observations in two spatial dimensions that allows for evaluation of the log-likelihood and its gradient (i.e., the score equations) in $\tilde{O}(n^{3/2})$ time under certain assumptions, where $n$ is the number of observations. Our method relies on the skeletonization procedure described by Martinsson & Rokhlin in the form of the recursive skeletonization factorization of Ho & Ying. Combining this with an adaptation of the matrix peeling algorithm of Lin et al. for constructing $\mathcal{H}$-matrix representations of black-box operators, we obtain a framework that can be used in the context of any first-order optimization routine to quickly and accurately compute maximum-likelihood estimates.

36 pages, 8 figures

References in corpus (2)

• Nonstationary covariance models for global data
• A recursive skeletonization factorization based on strong admissibility

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