Sampling Gaussian Distributions in Krylov Spaces with Conjugate Gradients
Sampling Gaussian Distributions in Krylov Spaces with Conjugate Gradients
复制标题
使用共轭梯度对 Krylov 空间中的高斯分布进行采样
DOI：
10.1137/110831404
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
C. Fox
中科院分区：
文献类型：
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作者：
Albert E. Parker;C. Fox
本文介绍了一种共轭梯度采样器，它是求解线性方程组的共轭梯度法（CG）的简单推广。CG采样器使用对称正定协方差或精度矩阵（以更便于建模者为准）从高斯概率密度迭代生成样本。与Lanczos方法解决特征值问题的方式类似，CG采样器在小维Krylov空间中近似协方差或精度矩阵。与任何迭代方法一样，CG采样器对于形成协方差或精度矩阵不切实际但通过矩阵操作是可行的高维问题是有效的。在精确算术中，采样器生成高斯样本，其实现的协方差收敛到感兴趣的协方差。在有限精度下，采样器产生具有实现协方差的高斯样本，该实现协方差是较小维度Krylov空间中所需协方差的最佳近似。...
This paper introduces a conjugate gradient sampler that is a simple extension of the method of conjugate gradients (CG) for solving linear systems. The CG sampler iteratively generates samples from a Gaussian probability density, using either a symmetric positive definite covariance or precision matrix, whichever is more convenient to model. Similar to how the Lanczos method solves an eigenvalue problem, the CG sampler approximates the covariance or precision matrix in a small dimensional Krylov space. As with any iterative method, the CG sampler is efficient for high dimensional problems where forming the covariance or precision matrix is impractical, but operating by the matrix is feasible. In exact arithmetic, the sampler generates Gaussian samples with a realized covariance that converges to the covariance of interest. In finite precision, the sampler produces a Gaussian sample with a realized covariance that is the best approximation to the desired covariance in the smaller dimensional Krylov space. ...