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Sparsistency and agnostic inference in sparse PCA
- Source :
- Annals of Statistics 2015, Vol. 43, No. 1, 299-322
- Publication Year :
- 2014
-
Abstract
- The presence of a sparse "truth" has been a constant assumption in the theoretical analysis of sparse PCA and is often implicit in its methodological development. This naturally raises questions about the properties of sparse PCA methods and how they depend on the assumption of sparsity. Under what conditions can the relevant variables be selected consistently if the truth is assumed to be sparse? What can be said about the results of sparse PCA without assuming a sparse and unique truth? We answer these questions by investigating the properties of the recently proposed Fantope projection and selection (FPS) method in the high-dimensional setting. Our results provide general sufficient conditions for sparsistency of the FPS estimator. These conditions are weak and can hold in situations where other estimators are known to fail. On the other hand, without assuming sparsity or identifiability, we show that FPS provides a sparse, linear dimension-reducing transformation that is close to the best possible in terms of maximizing the predictive covariance.<br />Comment: Published in at http://dx.doi.org/10.1214/14-AOS1273 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
- Subjects :
- Mathematics - Statistics Theory
Statistics - Machine Learning
Subjects
Details
- Database :
- arXiv
- Journal :
- Annals of Statistics 2015, Vol. 43, No. 1, 299-322
- Publication Type :
- Report
- Accession number :
- edsarx.1401.6978
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1214/14-AOS1273