A coordinate majorization descent algorithm for ℓ1 penalized learning

Yi Yang, Hui Zou

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The glmnet package by Friedman et al. [Regularization paths for generalized linear models via coordinate descent, J. Statist. Softw. 33 (2010), pp. 1-22] is an extremely fast implementation of the standard coordinate descent algorithm for solving ℓ1 penalized learning problems. In this paper, we consider a family of coordinate majorization descent algorithms for solving the ℓ1 penalized learning problems by replacing each coordinate descent step with a coordinate-wise majorization descent operation. Numerical experiments show that this simple modification can lead to substantial improvement in speed when the predictors have moderate or high correlations.

Original languageEnglish (US)
Pages (from-to)84-95
Number of pages12
JournalJournal of Statistical Computation and Simulation
Issue number1
StatePublished - Jan 2014

Bibliographical note

Funding Information:
The authors thank the editor, an associate editor and referee for their helpful comments and suggestions. This work is supported in part by NSF Grant DMS-08-46068.


  • coordinate decent
  • glmnet
  • lasso
  • majorization-minimization


Dive into the research topics of 'A coordinate majorization descent algorithm for ℓ1 penalized learning'. Together they form a unique fingerprint.

Cite this