Using the ℓ1-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
