Numerical Tolerance for Spectral Decompositions of Random Matrices and Applications to Network Inference
量化了随机矩阵特征分解中统计误差对数值近似质量的影响，提出最优数值容差，使算法在数值误差与统计误差相当时终止，节省计算且不损失精度，并通过模拟和真实网络分析验证了该准则对后续推断的重要性。
We precisely quantify the impact of statistical error in the quality of a numerical approximation to a random matrix eigendecomposition, and under mild conditions, we use this to introduce an optimal numerical tolerance for residual error in spectral decompositions of random matrices. We demonstrate that terminating an eigendecomposition algorithm when the numerical error and statistical error are of the same order results in computational savings with no loss of accuracy. We illustrate the practical consequences of our stopping criterion with an analysis of simulated and real networks. Our theoretical results and real-data examples establish that the tradeoff between statistical and numerical error is of significant importance for subsequent inference.