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Title: Optimal Structured Principal Subspace Estimation: Metric Entropy and Minimax Rates
Driven by a wide range of applications, several principal subspace estimation problems have been studied individually under different structural constraints. This paper presents a uni- fied framework for the statistical analysis of a general structured principal subspace estima- tion problem which includes as special cases sparse PCA/SVD, non-negative PCA/SVD, subspace constrained PCA/SVD, and spectral clustering. General minimax lower and up- per bounds are established to characterize the interplay between the information-geometric complexity of the constraint set for the principal subspaces, the signal-to-noise ratio (SNR), and the dimensionality. The results yield interesting phase transition phenomena concern- ing the rates of convergence as a function of the SNRs and the fundamental limit for consistent estimation. Applying the general results to the specific settings yields the mini- max rates of convergence for those problems, including the previous unknown optimal rates for sparse SVD, non-negative PCA/SVD and subspace constrained PCA/SVD.  more » « less
Award ID(s):
2015259
NSF-PAR ID:
10285915
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of machine learning research
Volume:
22
ISSN:
1532-4435
Page Range / eLocation ID:
1-45
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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