Variance Reduction for Matrix Computations with Applications to Gaussian Processes

In addition to recent developments in computing speed and memory, methodological advances have contributed significant gains the performance of stochastic simulation. this paper, we focus on variance reduction for matrix computations via factorization. We provide insights into existing methods estimating entries large matrices. Popular do not exploit that is possible when factorized. show how square root factorization can achieve some important cases arbitrarily better performance. addition, propose a factorized estimator trace product matrices numerically demonstrate be up 1,000 times more efficient certain problems log-likelihood Gaussian process. Additionally, new log-determinant positive semi-definite where treated as normalizing constant probability density.