What is it about?
This work gives answers how to approximate large covariance matrices; how to infer unknown parameters from large data sets; how to approximate joint Gaussian log-likelihood. Matrices could be unstructured, observations could be collected in irregular locations. This work extends known O(nlog n) algorithms for circulant matrices to more general matrices.
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Why is it important?
This is a relative new technique, initially developed by Hackbusch'99 for solving differential and integral equations with O(n log n) computational and storage cost. In this work we apply this techniques to typical statistical tasks.
Perspectives
This work allows to consider very large data sets (e.g., 2.000.000 irregular locations and non-homogeneous covariance functions). We hope that this research will motivate others to consider new classes of more complicated inhomogeneous covariance functions. Since the numerical complexity of linear algebra algorithms drops from O(n^3) to O(n log n), the larger (multiscale or high-dimensional) problems could be solved.
Dr. Alexander Litvinenko
Rheinisch Westfalische Technische Hochschule Aachen
Read the Original
This page is a summary of: Likelihood approximation with hierarchical matrices for large spatial datasets, Computational Statistics & Data Analysis, September 2019, Elsevier,
DOI: 10.1016/j.csda.2019.02.002.
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