English

Trace Lasso: a trace norm regularization for correlated designs

Machine Learning 2011-09-14 v1 Machine Learning

Abstract

Using the 1\ell_1-norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account the correlation of the design matrix to stabilize the estimation. This norm, called the trace Lasso, uses the trace norm, which is a convex surrogate of the rank, of the selected covariates as the criterion of model complexity. We analyze the properties of our norm, describe an optimization algorithm based on reweighted least-squares, and illustrate the behavior of this norm on synthetic data, showing that it is more adapted to strong correlations than competing methods such as the elastic net.

Keywords

Cite

@article{arxiv.1109.1990,
  title  = {Trace Lasso: a trace norm regularization for correlated designs},
  author = {Edouard Grave and Guillaume Obozinski and Francis Bach},
  journal= {arXiv preprint arXiv:1109.1990},
  year   = {2011}
}
R2 v1 2026-06-21T19:02:30.437Z