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2009

On the Peaking Phenomenon of the Lasso in Model Selection

Kraemer, Nicole

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I briefly report on some unexpected results that I obtained when optimizing the model parameters of the Lasso.

In simulations with varying observations-to-variables ratio n=p, I typically observe a strong peak in the test error curve at the transition point n/p = 1.
This peaking phenomenon is well-documented in scenarios that involve the inversion of the sample covariance matrix, and as I illustrate in this note, it is also the source of the peak for the Lasso.
The key problem is the parametrization of the Lasso penalty (as e.g.

On the Peaking Phenomenon of the Lasso in Model Selection · Around

Built on

Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · 1996
Earlier work this paper cites.
Expected classification error of the Fisher linear classifier with pseudo-inverse covariance matrix
Raudys, S. and Duin, R. (1998) · 1998
Earlier work this paper cites.
Learning to Generalize
Opper, M. (2001) · 2001
Earlier work this paper cites.

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