SOFAR: Large-Scale Association Network Learning

Yoshimasa Uematsu, Yingying Fan, Kun Chen, Jinchi Lv, Wei Lin

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsity and orthogonality have been two largely incompatible goals. To accommodate both features, in this paper, we suggest the method of sparse orthogonal factor regression (SOFAR) via the sparse singular value decomposition with orthogonality constrained optimization to learn the underlying association networks, with broad applications to both unsupervised and supervised learning tasks, such as biclustering with sparse singular value decomposition, sparse principal component analysis, sparse factor analysis, and spare vector autoregression analysis. Exploiting the framework of convexity-assisted nonconvex optimization, we derive nonasymptotic error bounds for the suggested procedure characterizing the theoretical advantages. The statistical guarantees are powered by an efficient SOFAR algorithm with convergence property. Both computational and theoretical advantages of our procedure are demonstrated with several simulations and real data examples.

Original languageEnglish
Article number8685192
Pages (from-to)4924-4939
Number of pages16
JournalIEEE Transactions on Information Theory
Volume65
Issue number8
DOIs
Publication statusPublished - 2019

Keywords

  • Big data
  • large-scale association network
  • latent factors
  • nonconvex statistical learning
  • orthogonality constrained optimization
  • simultaneous response and predictor selection
  • sparse singular value decomposition

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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