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.
翻译:我们用对正确定系数矩阵分析基列洛夫以前的BayesCG的校准,这是共振梯度法(CG)解决线性方程系统的概率数字延伸,它具有正对正确定系数矩阵。校准是指求解器产生的后方变量的统计质量。由于BayesCG没有按照严格的现有概念加以校准,我们建议采用两个必要的但不足以校准的测试统计数据:Z-统计学和新的S-统计学。我们从分析和实验上表明,在低级别近Krylov 后方方程式下,BayesCG展示了校准求解器的可取性能,只是略为乐观,在计算上与CG具有竞争力。