Assistant professor of Statistics at the University of Texas at Austin
Title: Bootstrapping the Error of Oja's Algorithm
Abstract: We consider the problem of quantifying uncertainty for the estimation error of the leading eigenvector from Oja's algorithm for streaming Principal Component Analysis, where the data are generated IID from some unknown distribution. By combining classical tools from the U-statistics literature with recent results on high-dimensional central limit theorems of quadratic forms of random vectors and concentration of matrix products, we establish a Gaussian approximation result for the sin squared distance between the population eigenvector and the output of Oja’s algorithm. Since estimating the covariance matrix associated with the approximating distribution requires knowledge of unknown model parameters, we propose a multiplier bootstrap algorithm that may be updated in an online manner. We establish conditions under which the bootstrap distribution is close to the corresponding sampling distribution with high probability, thereby establishing the bootstrap as a consistent inferential method in an appropriate asymptotic regime.
This Colloquium will be held on line/Zoom, Friday, October 8th - at 2:00PM
Topic: Statistics Colloquium Fall 2021
Time: This is a recurring meeting Meet anytime
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Meeting ID: 913 7582 2348