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Activity Number: 357 - Contemporary Multivariate Methods
Type: Contributed
Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #313766
Title: Numerical Tolerance for Spectral Decompositions of Random Matrices
Author(s): Zachary Lubberts* and Avanti Athreya and Vince Lyzinski and Minh Tang and Carey Priebe and Michael J Kane and Youngser Park and Bryan Lewis
Companies: Johns Hopkins University and Johns Hopkins University and University of Maryland College Park and NC State University and Johns Hopkins University and Yale University School of Public Health and Johns Hopkins University and Independent Researcher
Keywords: statistical error; numerical error; optimal error tolerance; random matrix; spectral decomposition

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 import for data science.

Authors who are presenting talks have a * after their name.

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