AMS Weekly Seminar w/ Zachary Lubberts (AMS) on Zoom

Title: Numerical tolerance for spectral decompositions of random matrices
 
Abstract: The computation of parametric estimates often involves iterative numerical approximations, which introduce numerical error. But when these estimates depend on random observations, they necessarily involve statistical error as well. Thus the common approach of minimizing numerical error without accounting for inherent statistical error can be both costly and wasteful, since it results in no improvement to the estimator’s accuracy. We quantify this tradeoff between numerical and statistical error in a problem of estimating the eigendecomposition for the mean of a random matrix from its observed value, and show that one can save significant computation by terminating the iterative procedure early, with no loss of accuracy. We demonstrate this in a setting of estimating the latent positions of a random network from the observed adjacency matrix, on real and simulated data.
 
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Topic: AMS Department Seminar (Fall 2020)
Date: Sep 10, 2020 12:18 PM Eastern Time (US and Canada)
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