On the Peaking Phenomenon of the Lasso in Model Selection

Details On the Peaking Phenomenon of the Lasso in Model Selection On the Peaking Phenomenon of the Lasso in Model Selection

2009-04-28

arxiv.org/abs/0904.4416v1

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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. in the current R package lars) and I present a solution in terms of a normalized Lasso parameter.

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