Online Program

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Saturday, May 19
Machine Learning
Machine Learning for Complex Data
Sat, May 19, 10:30 AM - 12:00 PM
Grand Ballroom D
 

The Two-to-Infinity Norm and Singular Subspace Geometry With Applications to High-Dimensional Statistics (304578)

*Joshua Cape, Johns Hopkins University 
Carey E. Priebe, Johns Hopkins University 
Minh Tang, Johns Hopkins University 

Keywords: spectral methods, dimension reduction, subspace estimation, singular value decomposition

The singular value matrix decomposition plays a ubiquitous role throughout statistics and data science. Myriad applications including clustering, classification, and dimensionality reduction involve studying and exploiting the geometric structure of singular values and singular vectors. We provide a novel collection of technical and theoretical tools for studying the geometry of singular subspaces using the two-to-infinity norm. Motivated by preliminary deterministic Procrustes analysis, we consider a general matrix perturbation setting in which we derive a new Procrustean matrix decomposition. Together with flexible machinery developed for the two-to-infinity norm, this allows for a refined analysis of the induced perturbation geometry with respect to the underlying singular vectors even in the presence of singular value multiplicity. Our analysis yields perturbation bounds for a range of popular matrix noise models, each of which has a meaningful associated statistical inference task. Specific applications include the problem of covariance matrix estimation, singular subspace recovery, and multiple graph inference.