Asymptotic Theory for Estimating the Singular Vectors and Values of a Partially-observed Low Rank Matrix with Noise

Cited 2 time in webofscience Cited 0 time in scopus
  • Hit : 277
  • Download : 0
Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for statistical analyses and inferences. This paper proposes estimators of these quantities and studies their asymptotic behavior. Under the setting where the dimensions of the matrix increase to infinity and the probability of observing each entry is identical, Theorem 1 gives the rate of convergence for the estimated singular vectors; Theorem 3 gives a multivariate central limit theorem for the estimated singular values. Even though the estimators use only a partially observed matrix, they achieve the same rates of convergence as the fully observed case. These estimators combine to form a consistent estimator of the full low rank matrix that is computed with a non-iterative algorithm. In the cases studied in this paper, this estimator achieves the minimax lower bound in Koltchinskii, Lounici and Tsybakov (2011). The numerical experiments corroborate our theoretical results.
Publisher
STATISTICA SINICA
Issue Date
2017-11
Language
English
Article Type
Article
Keywords

RELATIVE PERTURBATION-THEORY; COMPLETION; PENALIZATION

Citation

STATISTICA SINICA, v.27, pp.1921 - 1948

ISSN
1017-0405
DOI
10.5705/ss.202016.0205
URI
http://hdl.handle.net/10203/237195
Appears in Collection
MT-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 2 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0