Parallel Matrix Condensation for Calculating Log-Determinant of Large Matrix

Xiaomeng Dong, EN Barnett, Sudarshan K. Dhall

Calculating the log-determinant of a matrix is useful for statistical computations used in machine learning, such as generative learning which uses the log-determinant of the covariance matrix to calculate the log-likelihood of model mixtures. The log-determinant calculation becomes challenging as the number of variables becomes large. Therefore, finding a practical speedup for this computation can be useful. In this study, we present a parallel matrix condensation algorithm for calculating the log-determinant of a large matrix. We demonstrate that in a distributed environment, Parallel Matrix Condensation has several advantages over the well-known Parallel Gaussian Elimination. The advantages include high data distribution efficiency and less data communication operations. We test our Parallel Matrix Condensation against self-implemented Parallel Gaussian Elimination as well as ScaLAPACK (Scalable Linear Algebra Package) on 1000 x1000 to 8000x8000 for 1,2,4,8,16,32,64 and 128 processors. The results show that Matrix Condensation yields the best speed-up among all other tested algorithms. The code is available on https://github.com/vbvg2008/MatrixCondensation

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