论文标题
概率数字线性求解器Bayescg的统计特性
Statistical Properties of the Probabilistic Numeric Linear Solver BayesCG
论文作者
论文摘要
我们分析了Krylov Prior的贝内斯校准的校准，这是求解具有对称正定系数矩阵的线性方程系统的共轭梯度（CG）方法的概率数字扩展。校准是指求解器产生的后协方差的统计质量。由于在严格的现有概念中未经校准贝吉斯克，我们提出了两个必要但不足以进行校准的测试统计数据：Z统计和新的S统计量。我们通过分析和实验表明，在低级别近似Krylov后期，贝内斯基表现出校准求解器的理想特性，仅略微乐观，并且与CG具有计算竞争性。
We analyse the calibration of BayesCG under the Krylov prior, a probabilistic numeric extension of the Conjugate Gradient (CG) method for solving systems of linear equations with symmetric positive definite coefficient matrix. Calibration refers to the statistical quality of the posterior covariances produced by a solver. Since BayesCG is not calibrated in the strict existing notion, we propose instead two test statistics that are necessary but not sufficient for calibration: the Z-statistic and the new S-statistic. We show analytically and experimentally that under low-rank approximate Krylov posteriors, BayesCG exhibits desirable properties of a calibrated solver, is only slightly optimistic, and is computationally competitive with CG.
