A DEFLATED VERSION OF THE BLOCK CONJUGATE GRADIENT ALGORITHM WITH AN APPLICATION TO GAUSSIAN PROCESS MAXIMUM LIKELIHOOD ESTIMATION
A DEFLATED VERSION OF THE BLOCK CONJUGATE GRADIENT ALGORITHM WITH AN APPLICATION TO GAUSSIAN PROCESS MAXIMUM LIKELIHOOD ESTIMATION
复制标题
分块共轭梯度算法的精简版及其在高斯过程最大似然估计中的应用
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Jie Chen
中科院分区：
文献类型：
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作者：
Jie Chen
许多统计应用需要对称正定协方差矩阵的解，有时具有大量统计独立性的右侧。通过预处理，除了少数极端特征值迅速偏离范围外，预处理后的矩阵几乎所有特征值都聚集在一个很窄的范围内。我们推导出一个紧缩版本的块共轭梯度算法来处理极端的特征值和多个右手边。在适当的收缩下，收敛速度取决于聚类特征值的分布，而不是极值。高斯过程最大似然估计应用中的数值实验表明，所提出的求解器的有效性，指出解决非常大规模的，现实生活中的数据分析问题的潜力。
Many statistical applications require the solution of a symmetric positive definite covariance matrix, sometimes with a large number of right-hand sides of a statistical independence nature. With preconditioning, the preconditioned matrix has almost all the eigenvalues clustered within a narrow range, except for a few extreme eigenvalues deviating from the range rapidly. We derive a deflated version of the block conjugate gradient algorithm to handle the extreme eigenvalues and the multiple right-hand sides. With an appropriate deflation, the rate of convergence depends on the spread of the clustered eigenvalues but not the extreme ones. Numerical experiments in a Gaussian process maximum likelihood estimation application demonstrate the effectiveness of the proposed solver, pointing to the potential of solving very large scale, real-life data analysis problems.