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Activity Number: 438
Type: Contributed
Date/Time: Tuesday, August 2, 2016 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #319430
Title: Optimal Detection of Weak Principal Components in High-Dimensional Data
Author(s): Edgar Dobriban*
Companies:
Keywords: principal component analysis ; random matrix theory ; high-dimensional statistics ; spiked model ; linear spectral statistics
Abstract:

Principal component analysis is a widely used method for dimension reduction. In high dimensional data, the ``signal'' eigenvalues corresponding to weak principal components (PCs) do not necessarily separate from the bulk of the ``noise'' eigenvalues. In this setting, it is not possible to decide based on the largest eigenvalue alone whether or not there are "signal" PCs in the data. In this talk we explore this phenomenon in a general model that captures the shape of eigenvalue distributions often seen in applications. We show how to construct statistical tests to detect principal components, based on all eigenvalues. We also explain how recent computational advances in random matrix theory enable the efficient implementation of our methods.


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

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