Likelihood approximation with hierarchical matrices for large spatial datasets
By Alexander Litvinenko, Ying Sun, Marc G. Genton, David E. Keyes. 2017
56 citations recorded by the source corpus.
We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the linear algebra, we approximate the discretized covariance function in the hierarchical (H-) matrix format. The H-matrix format has a log-linear computational cost and storage $O(kn \log n)$, where the rank $k$ is a small integer and $n$ is the number of locations. The H-matrix technique allows us to work with general covariance matrices in an efficient way, since H-matrices can approximate inhomogeneous covariance functions, with a fairly general mesh that is not necessarily axes-parallel, and neither the covariance matrix itself nor its inverse have to be sparse. We demonstrate our method with Monte Carlo simulations and an application to soil moisture data. The C, C++ codes and data are freely available.
Subfields: Civil and Structural Engineering, Environmental Engineering
How researchers see this paper
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In Civil and Structural Engineering
- G. Em Karniadakis
- Abhirup Datta
- Robert B. Gramacy
- Anthony Nouy
- Xiaoliang Wan
- Dongbin Xiu
- Nicholas Zabaras
- Xiang Ma
In Environmental Engineering
- Reinhard Furrer
- Robert B. Gramacy
- Abhirup Datta
- Joseph Guinness
- Matthias Katzfuss
- Andrew O. Finley
- G. Em Karniadakis
- Finn Lindgren
Citations in the corpus
- Neural-net-induced Gaussian process regression for function approximation and PDE solution (2018, background): “In future work, we intend to leverage scalable GPs recently developed in [22, 23, 24] to tackle large dataset problems.”
- A Case Study Competition Among Methods for Analyzing Large Spatial Data (2017, methodology): “This study, while thorough, is non-comprehensive in that other methods for large spatial data (e.g., Sang and Huang 2012; Stein et al. 2013; Kleiber and Nychka 2015; CastrillonCandás et al. 2016; Sun and Stein 2016; Litvinenko et al. 2017) were not included.”