Sparse Precision Matrix Selection for Fitting Gaussian Random Field
Models to Large Data Sets
release_hkvexikdtbg6fjmfmja3jo227i
by
Sam Davanloo Tajbakhsh, Necdet Serhat Aybat, Enrique Del Castillo
2015
Abstract
Iterative methods for fitting a Gaussian Random Field (GRF) model to spatial
data via maximum likelihood (ML) require O(n^3) floating point
operations per iteration, where n denotes the number of data locations. For
large data sets, the O(n^3) complexity per iteration together with
the non-convexity of the ML problem render traditional ML methods inefficient
for GRF fitting. The problem is even more aggravated for anisotropic GRFs where
the number of covariance function parameters increases with the process domain
dimension. In this paper, we propose a new two-step GRF estimation procedure
when the process is second-order stationary. First, a convex likelihood
problem regularized with a weighted ℓ_1-norm, utilizing the available
distance information between observation locations, is solved to fit a sparse
precision (inverse covariance) matrix to the observed data using the
Alternating Direction Method of Multipliers. Second, the parameters of the GRF
spatial covariance function are estimated by solving a least squares problem.
Theoretical error bounds for the proposed estimator are provided; moreover,
convergence of the estimator is shown as the number of samples per location
increases. The proposed method is numerically compared with state-of-the-art
methods for big n. Data segmentation schemes are implemented to handle large
data sets.
In text/plain
format
Archived Files and Locations
application/pdf 1.2 MB
file_zv7f36m3krapnkfxpwruetcgjm
|
arxiv.org (repository) web.archive.org (webarchive) |
1405.5576v3
access all versions, variants, and formats of this works (eg, pre-prints)