Three structural results on the lasso problem

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

The lasso problem, least squares with a ℓ1 regularization penalty, has been very successful as a tool for obtaining sparse representations of data in terms of given dictionary. It is known, but not widely appreciated, that the lasso problem need not have a unique solution. Sufficient conditions which ensure uniqueness of the solution are known but necessary and sufficient conditions have been elusive. We present three structural results on the lasso problem. First, we show that when the dictionary has more columns than rows, it is always possible to ensure that the dictionary has full row rank. Next we show that the feasible set for the dual lasso problem is bounded if and only if the dictionary has full row rank. Lastly, we give necessary and sufficient conditions for the uniqueness of a lasso solution.

Original languageEnglish (US)
Title of host publication2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings
Pages3392-3396
Number of pages5
DOIs
StatePublished - Oct 18 2013
Event2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Vancouver, BC, Canada
Duration: May 26 2013May 31 2013

Other

Other2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013
CountryCanada
CityVancouver, BC
Period5/26/135/31/13

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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