2011/08/31 by Marco Selig, Niels Oppermann, Torsten A. Enßlin +1 · 14 citations
Engineering · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Autocorrelation #Autocorrelation matrix #Computer science #Diagonal #Diagonal matrix #Geometry #Inference #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Operator (biology) #Sparse and Compressive Sensing Techniques #Speedup #Statistical Mechanics and Entropy #Statistical and numerical algorithms #Statistical inference #Statistics #astro-ph.IM #stat.ME
paper · pdf · doi:10.1103/physreve.85.021134
published in Physical Review E 85(2), 021134 (American Physical Society) · 9 pages, 6 figures, accepted by Phys. Rev. E; introduction revised, results unchanged; page proofs implemented
openalex publication_date 2012/02/23 · arxiv created 2012/02/24 · arxiv updated 2015/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image reconstruction and statistical inference. Here, methods of statistical inference are used to improve the accuracy or the computational costs of matrix probing methods to estimate matrix diagonals. In particular, the generalized Wiener filter methodology, as developed within information field theory, is shown to significantly improve estimates based on only a few sampling probes, in cases in which some form of continuity of the solution can be assumed. The strength, length scale, and precise functional form of the exploited autocorrelation function of the matrix diagonal is determined from the probes themselves. The developed algorithm is successfully applied to mock and real world problems. These performance tests show that, in situations where a matrix diagonal has to be calculated from only a small number of computationally expensive probes, a speedup by a factor of 2 to 10 is possible with the proposed method.