TY - DATA T1 - Efficient Covariance Approximations for Large Sparse Precision Matrices PY - 2018/07/11 AU - Per Sidén AU - Finn Lindgren AU - David Bolin AU - Mattias Villani UR - https://tandf.figshare.com/articles/dataset/Efficient_Covariance_Approximations_for_Large_Sparse_Precision_Matrices/6804491 DO - 10.6084/m9.figshare.6804491.v1 L4 - https://ndownloader.figshare.com/files/12375614 L4 - https://ndownloader.figshare.com/files/12375617 L4 - https://ndownloader.figshare.com/files/12375620 L4 - https://ndownloader.figshare.com/files/12375623 L4 - https://ndownloader.figshare.com/files/12375629 L4 - https://ndownloader.figshare.com/files/12375632 L4 - https://ndownloader.figshare.com/files/12375635 L4 - https://ndownloader.figshare.com/files/12375638 L4 - https://ndownloader.figshare.com/files/12375641 L4 - https://ndownloader.figshare.com/files/12375644 L4 - https://ndownloader.figshare.com/files/12375647 L4 - https://ndownloader.figshare.com/files/12375650 L4 - https://ndownloader.figshare.com/files/12375653 L4 - https://ndownloader.figshare.com/files/12375656 L4 - https://ndownloader.figshare.com/files/12375659 L4 - https://ndownloader.figshare.com/files/12375662 L4 - https://ndownloader.figshare.com/files/12375665 L4 - https://ndownloader.figshare.com/files/12375668 L4 - https://ndownloader.figshare.com/files/12375671 KW - resonance imaging data KW - approximation KW - application KW - Large Sparse Precision Matrices KW - Efficient Covariance Approximations KW - covariance matrix KW - Rao-Blackwellized Monte Carlo sampling-based method N2 - The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the covariance matrix, such as the marginal variances, which may be non-trivial to obtain when the dimension is large. This paper introduces a fast Rao-Blackwellized Monte Carlo sampling-based method for efficiently approximating selected elements of the covariance matrix. The variance and confidence bounds of the approximations can be precisely estimated without additional computational costs. Furthermore, a method that iterates over subdomains is introduced, and is shown to additionally reduce the approximation errors to practically negligible levels in an application on functional magnetic resonance imaging data. Both methods have low memory requirements, which is typically the bottleneck for competing direct methods. ER -