High dimensional variable selection via tilting

Haeran Cho, Piotr Fryzlewicz*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

43 Citations (Scopus)

Abstract

The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly spurious) high correlations between the variables, which result in marginal correlation being unreliable as a measure of association between the variables and the response. We propose a new way of measuring the contribution of each variable to the response which takes into account high correlations between the variables in a data-driven way. The proposed tilting procedure provides an adaptive choice between the use of marginal correlation and tilted correlation for each variable, where the choice is made depending on the values of the hard thresholded sample correlation of the design matrix. We study the conditions under which this measure can successfully discriminate between the relevant and the irrelevant variables and thus be used as a tool for variable selection. Finally, an iterative variable screening algorithm is constructed to exploit the theoretical properties of tilted correlation, and its good practical performance is demonstrated in a comparative simulation study.

Original languageEnglish
Pages (from-to)593-622
Number of pages30
JournalJournal of the Royal Statistical Society: Series B
Volume74
Issue number3
Early online date15 Feb 2012
DOIs
Publication statusPublished - Jun 2012

Keywords

  • Variable selection
  • Linear regression
  • High dimensionality
  • ORACLE PROPERTIES
  • MODEL SELECTION
  • GRAPHS
  • Adaptivity
  • Correlation
  • DISCOVERY
  • LASSO
  • Hard thresholding
  • FEATURE SPACE
  • CLASSIFICATION
  • NONCONCAVE PENALIZED LIKELIHOOD
  • REGRESSION
  • SHRINKAGE

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