, Volume 24, Issue 2, pp 247-263

Parameter estimation in high dimensional Gaussian distributions

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Abstract

In order to compute the log-likelihood for high dimensional Gaussian models, it is necessary to compute the determinant of the large, sparse, symmetric positive definite precision matrix. Traditional methods for evaluating the log-likelihood, which are typically based on Cholesky factorisations, are not feasible for very large models due to the massive memory requirements. We present a novel approach for evaluating such likelihoods that only requires the computation of matrix-vector products. In this approach we utilise matrix functions, Krylov subspaces, and probing vectors to construct an iterative numerical method for computing the log-likelihood.