Adaptive Lasso based on joint M-estimation of regression and scale

Esa Ollila*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

3 Citations (Scopus)


The adaptive Lasso (Least Absolute Shrinkage and Selection Operator) obtains oracle variable selection property by using cleverly chosen adaptive weights for regression coefficients in the 1-penalty. In this paper, in the spirit of M-estimation of regression, we propose a class of adaptive M-Lasso estimates of regression and scale as solutions to generalized zero subgradient equations. The defining estimating equations depend on a differentiable convex loss function and choosing the LS-loss function yields the standard adaptive Lasso estimate and the associated scale statistic. An efficient algorithm, a generalization of the cyclic coordinate descent algorithm, is developed for computing the proposed M-Lasso estimates. We also propose adaptive MLasso estimate of regression with preliminary scale estimate that uses a highly-robust bounded loss function. A unique feature of the paper is that we consider complex-valued measurements and regression parameter. Consistent variable selection property of the adaptive M-Lasso estimates are illustrated with a simulation study.

Original languageEnglish
Title of host publicationProceedings of the 24th European Signal Processing Conference, EUSIPCO 2016
Number of pages5
ISBN (Electronic)9780992862657
Publication statusPublished - 28 Nov 2016
MoE publication typeA4 Article in a conference publication
EventEuropean Signal Processing Conference - Budapest, Hungary
Duration: 28 Aug 20162 Sep 2016
Conference number: 24

Publication series

NameEuropean Signal Processing Conference
PublisherInstitute of Electrical and Electronics Engineers, Inc.
ISSN (Print)2219-5491
ISSN (Electronic)2076-1465


ConferenceEuropean Signal Processing Conference
Abbreviated titleEUSIPCO
Internet address


  • Adaptive Lasso
  • M-estimation
  • Penalized regression
  • Sparsity
  • Variable selection

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