Parameter estimation in high dimensional Gaussian distributions

被引:35
作者
Aune, Erlend [1 ]
Simpson, Daniel P. [1 ]
Eidsvik, Jo [1 ]
机构
[1] Norwegian Univ Sci & Technol, N-7034 Trondheim, Norway
关键词
Gaussian distribution; Krylov methods; Matrix functions; Numerical linear algebra; Estimation; MARKOV RANDOM-FIELDS; MATRIX FUNCTIONS; LIKELIHOOD; MODELS; BOUNDS;
D O I
10.1007/s11222-012-9368-y
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
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.
引用
收藏
页码:247 / 263
页数:17
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