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2016
ACM

Fast covariance estimation for high-dimensional functional data

4 years 3 months ago
Fast covariance estimation for high-dimensional functional data
For smoothing covariance functions, we propose two fast algorithms that scale linearly with the number of observations per function. Most available methods and software cannot smooth covariance matrices of dimension J ×J with J > 500; the recently introduced sandwich smoother is an exception, but it is not adapted to smooth covariance matrices of large dimensions such as J ≥ 10, 000. Covariance matrices of order J = 10, 000, and even J = 100, 000, are becoming increasingly common, e.g., in 2- and 3-dimensional medical imaging and high-density wearable sensor data. We introduce two new algorithms that can handle very large covariance matrices: 1) FACE: a fast implementation of the sandwich smoother and 2) SVDS: a two-step procedure that first applies singular value decomposition to the data matrix and then smoothes the eigenvectors. Compared to existing techniques, these new algorithms are at least an order of magnitude faster in high dimensions and drastically reduce memory req...
Luo Xiao, Vadim Zipunnikov, David Ruppert, Ciprian
Added 09 Apr 2016
Updated 09 Apr 2016
Type Journal
Year 2016
Where SAC
Authors Luo Xiao, Vadim Zipunnikov, David Ruppert, Ciprian M. Crainiceanu
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