Screening Tests for Lasso Problems

Zhen James Xiang, Yun Wang, Peter Jeffrey Ramadge

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

This paper is a survey of dictionary screening for the lasso problem. The lasso problem seeks a sparse linear combination of the columns of a dictionary to best match a given target vector. This sparse representation has proven useful in a variety of subsequent processing and decision tasks. For a given target vector, dictionary screening quickly identifies a subset of dictionary columns that will receive zero weight in a solution of the corresponding lasso problem. These columns can be removed from the dictionary prior to solving the lasso problem without impacting the optimality of the solution obtained. This has two potential advantages: it reduces the size of the dictionary, allowing the lasso problem to be solved with less resources, and it may speed up obtaining a solution. Using a geometrically intuitive framework, we provide basic insights for understanding useful lasso screening tests and their limitations. We also provide illustrative numerical studies on several datasets.

Original languageEnglish (US)
Article number7469344
Pages (from-to)1008-1027
Number of pages20
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume39
Issue number5
DOIs
StatePublished - May 1 2017

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

Keywords

  • Sparse representation
  • dictionary screening
  • dual lasso
  • feature selection
  • lasso

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