Trace Lasso: a trace norm regularization for correlated designs - Archive ouverte HAL Access content directly
Conference Papers Year : 2011

## Trace Lasso: a trace norm regularization for correlated designs

Edouard Grave
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Guillaume Obozinski
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Francis Bach
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#### Abstract

Using the $\ell_1$-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.

### Dates and versions

hal-00620197 , version 1 (09-09-2011)

### Identifiers

• HAL Id : hal-00620197 , version 1
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### Cite

Edouard Grave, Guillaume Obozinski, Francis Bach. Trace Lasso: a trace norm regularization for correlated designs. Neural Information Processing Systems (NIPS), 2012, Spain. ⟨hal-00620197⟩

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