Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity

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Schäfer, Florian; Sullivan, T. J.; Owhadi, Houman;
  • Subject: 65F30, 42C40, 65F50, 65N55, 65N75, 60G42, 68Q25, 68W40 | Computer Science - Computational Complexity | Computer Science - Data Structures and Algorithms | Mathematics - Probability | Mathematics - Numerical Analysis

Dense kernel matrices $\Theta \in \mathbb{R}^{N \times N}$ obtained from point evaluations of a covariance function $G$ at locations $\{ x_{i} \}_{1 \leq i \leq N}$ arise in statistics, machine learning, and numerical analysis. For covariance functions that are Green's ... View more
  • References (18)
    18 references, page 1 of 2

    M. Abramowitz and I. A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, volume 55 of National Bureau of Standards Applied Mathematics Series. U.S. Government Printing O ce, Washington, D.C., 1964.

    R. A. Adams and J. J. F. Fournier. Sobolev Spaces, volume 140 of Pure and Applied Mathematics (Amsterdam). Elsevier/Academic Press, Amsterdam, second edition, 2003.

    S. Ambikasaran, D. Foreman-Mackey, L. Greengard, D. W. Hogg, and M. O'Neil. Fast direct methods for gaussian processes. IEEE Trans. Pattern Anal. Mach. Intell., 38(2):252{265, 2016. doi:10.1109/TPAMI.2015.2448083.

    M. Armstrong. Basic Linear Geostatistics. Springer-Verlag, Berlin Heidelberg, 1998. doi:10.1007/978-3- 642-58727-6.

    F. R. Bach and M. I. Jordan. Kernel independent component analysis. J. Mach. Learn. Res., 3(1):1{48, 2003. doi:10.1162/153244303768966085.

    S. Banerjee, A. E. Gelfand, A. O. Finley, and H. Sang. Gaussian predictive process models for large spatial data sets. J. R. Stat. Soc. Ser. B Stat. Methodol., 70(4):825{848, 2008. doi:10.1111/j.1467- 9868.2008.00663.x.

    M. Bebendorf. Why nite element discretizations can be factored by triangular hierarchical matrices. SIAM J. Numer. Anal., 45(4):1472{1494, 2007. doi:10.1137/060669747.

    M. Bebendorf. Hierarchical Matrices, volume 63 of Lecture Notes in Computational Science and Engineering. Springer-Verlag, Berlin, 2008. doi:10.1007/978-3-540-77147-0.

    M. Bebendorf. Low-rank approximation of elliptic boundary value problems with high-contrast coe - cients. SIAM J. Math. Anal., 48(2):932{949, 2016. doi:10.1137/140991030.

    M. Bebendorf and S. Rjasanow. Adaptive low-rank approximation of collocation matrices. Computing, 70(1):1{24, 2003. doi:10.1007/s00607-002-1469-6.

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    nearLinKernel software on GitHub
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