DeepAI AI Chat
Log In Sign Up

Parallel Matrix Condensation for Calculating Log-Determinant of Large Matrix

11/20/2018
by   Xiaomeng Dong, et al.
0

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

READ FULL TEXT

page 1

page 2

page 3

page 4

09/08/2017

Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets

We use available measurements to estimate the unknown parameters (varian...
07/23/2019

ExaGeoStatR: A Package for Large-Scale Geostatistics in R

Parallel computing in Gaussian process calculation becomes a necessity f...
02/18/2020

Connecting MapReduce Computations to Realistic Machine Models

We explain how the popular, highly abstract MapReduce model of parallel ...
04/14/2021

Identification of unknown parameters and prediction with hierarchical matrices

Statistical analysis of massive datasets very often implies expensive li...
06/08/2018

A parallel algorithm for Gaussian elimination over finite fields

In this paper we describe a parallel Gaussian elimination algorithm for ...
07/29/2021

Calculating elements of matrix functions using divided differences

We introduce a method for calculating individual elements of matrix func...