论文标题
贝叶斯作为CG的不确定性意识
BayesCG As An Uncertainty Aware Version of CG
论文作者
论文摘要
贝叶斯结合梯度法（贝叶斯）是用于求解具有实际对称正定系数矩阵的线性系统的偶联梯度方法（CG）的概率概括。我们基于CG基于CG的贝叶斯在结构开发的先验分布下代表了CG的“不确定性意识”版本。它的输出由CG迭代和后协方差组成，可以传播到后续计算。协方差的排名低，并以各种形式保持。这可以轻松生成准确的样品，以探测下游计算中的不确定性。数值实验证实了低级后协方差的有效性。
The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of the Conjugate Gradient method (CG) for solving linear systems with real symmetric positive definite coefficient matrices. Our CG-based implementation of BayesCG under a structure-exploiting prior distribution represents an 'uncertainty-aware' version of CG. Its output consists of CG iterates and posterior covariances that can be propagated to subsequent computations. The covariances have low-rank and are maintained in factored form. This allows easy generation of accurate samples to probe uncertainty in downstream computations. Numerical experiments confirm the effectiveness of the low-rank posterior covariances.
