Noise Estimation in High-Dimensional PCA

• Activity Number: 331
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Didier Chetelat*+
• Companies: Cornell University
• Keywords: principal components analysis ; PCA ; covariance estimation ; unbiased risk estimator ; high dimension

Abstract

A popular model in high-dimensional Principal Components Analysis (PCA) is the spiked model, where a few eigenvalues are substantial while the others equal some small noise parameter. We propose to estimate this noise by variational optimization on the unbiased risk estimator of a natural loss. The resulting estimator turns out to possess a closed form solution and excellent theoretical behavior. To showcase performance, we use it to build a high-dimensional covariance estimator with substantial gains under spikedness, yet robustness against the assumption.