Fast spatial Gaussian process maximum likelihood estimation via skeletonization factorizations
Abstract
Maximum likelihood estimation for parameterfitting given observations from a Gaussian process in space is a computationallydemanding task that restricts the use of such methods to moderatelysized datasets. We present a framework for unstructured observations in two spatial dimensions that allows for evaluation of the loglikelihood 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 blackbox operators, we obtain a framework that can be used in the context of any firstorder optimization routine to quickly and accurately compute maximumlikelihood estimates.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 arXiv:
 arXiv:1603.08057
 Bibcode:
 2016arXiv160308057M
 Keywords:

 Statistics  Methodology;
 Mathematics  Numerical Analysis;
 60G15;
 65C60;
 65F30
 EPrint:
 36 pages, 8 figures