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What are the scenarios where Lasso is likely to perform better than Elastic Net (out of sample prediction)?

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  • $\begingroup$ The lasso is a special case of the elastic net $\endgroup$ – Stefan Wager Oct 29 '13 at 7:11
  • $\begingroup$ @StefanWager I'm aware of this. $\endgroup$ – user2763361 Oct 29 '13 at 7:14
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    $\begingroup$ Maybe one approach is to ask the opposite question: When does the elastic net beat the lasso by a lot? In general, if there is a group of highly correlated features, then the lasso will just pick one of the features and ignore the others. The elastic net, conversely, will tend to use all these features a little bit; this can be desirable from a generalization point of view. On the other hand, if your design matrix X is close to orthogonal, then there may be less reason to use an elastic net over the lasso. $\endgroup$ – Stefan Wager Oct 29 '13 at 7:26
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    $\begingroup$ @StefanWager Agreed. However my question is specified as it is intentionally -- all sources I read cover the relative benefits of Elastic Net but never the inverse. $\endgroup$ – user2763361 Oct 29 '13 at 7:30
  • $\begingroup$ @StefanWager Under what conditions will Elastic Net tend to push coefficients to 0.00000000 (like Lasso) versus the Ridge-like solution of 0.0019293? $\endgroup$ – user2763361 Oct 29 '13 at 7:36

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