Trace Lasso: a trace norm regularization for correlated designs
Machine Learning
2011-09-14 v1 Machine Learning
Abstract
Using the -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.
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}
}