Joshua Agterberg: Entrywise Estimation of Singular Vectors of Low-Rank Matrices with Heteroskedasticity and Dependence

/ January 10, 2022/

January 20, 2022 @ 3:00 pm – 3:30 pm

Abstract: We propose an estimator for the singular vectors of high-dimensional low-rank matrices corrupted by additive subgaussian noise, where the noise matrix is allowed to have dependence within rows and heteroskedasticity between them. We then study the statistical properties for the individual entries of our estimator, and we apply these results to high-dimensional mixture models. Our main result clearly shows the geometric relationship between the signal matrix, the covariance structure of the noise, and the distribution of the errors in the singular vector estimation task; moreover, our analysis depends only on the signal-to-noise ratio, the sample size, and the spectral properties of the signal matrix. We demonstrate our theoretical results through numerical simulations.

Bio: Joshua Agterberg is a PhD student in Applied Mathematics and Statistics at Johns Hopkins University, advised by Carey Priebe. His research interests include statistical network analysis, spectral methods, and high-dimensional statistics, with an emphasis on addressing theoretical problems in the mathematical and statistical foundations of data science. His work has been supported through a MINDS Fellowship and a Counselman Fellowship, and he is an Applied Mathematics and Statistics Teaching Fellow. In 2021 he received the Institute of Mathematical Statistics Hannan Award and a best presentation award for his talk and paper at the Joint Statistical Meetings student competition in nonparametric statistics.

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