What is it about?
We use hierarchical matrices to approximate the joint Gaussian log-likelihood function. The total cost is O(nlogn), much smaller than usual O(n^3). Among others we explain how to compute determinant and Cholesky factorization of large covariance matrix.
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Why is it important?
We can drastically reduce computing time and storage requirement in spatio-temporal statistics. With H-matrix techniques larger domains and time intervals can be researched. This will also reduce the finance cost of such research (e..g, weather prediction). The statistical model under investigation can be refined and its hyper-parameters improved.
Perspectives
With increasing volume of high-dimensional big data, I think, it is time to introduce to our colleagues from statistics the latest multi-linear algebra tools which were developed in our society. So that statisticians can significantly improve their statistical models.
Dr. Alexander Litvinenko
Rheinisch Westfalische Technische Hochschule Aachen
Read the Original
This page is a summary of: ℋ-matrix techniques for approximating large covariance matrices and estimating its parameters, PAMM, October 2016, Wiley,
DOI: 10.1002/pamm.201610354.
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