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I used cross validation to select lambda. Then I performed lasso and get non zero coefficients (features). Shall I perform cross validation for these non zero coefficients as a kind of validation?

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  • $\begingroup$ I am not clear about your question. What do you mean by "features selected by LASSO as a kind of validation for selected features". Also, I am not clear about "using different thresholds"? and also " input matrix for LASSO". I suggest you to ask your question in a more formal way. $\endgroup$ – TPArrow Apr 11 '16 at 12:28
  • $\begingroup$ I agree, your question is not clear at all. Perhaps you could provide a small working example? $\endgroup$ – StatGrrl Apr 11 '16 at 13:51
  • $\begingroup$ No, CV is enough. Unless you want to go back and do a different CV (ie 10-fold, etc). This would be a better way to "validate" your results if you feel uneasy. $\endgroup$ – jchaykow Apr 12 '16 at 3:50
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(Just guessing what you are actually asking)

Shall I perform cross validation for these non zero coefficients as a kind of validation

The final model (with the LASSO-determined coefficients) needs to have its own validation with a set of completely unknown cases in order to get a good estimate of its performance.

That is, if you do a cross validation for this final model validation step, you need to need to wrap another "outer" cross validation around all calculations that lead to the LASSO-model (including the "inner" cross validation you used for tuning of $\lambda$).

This is known and discussed here under the name of double cross validation or nested cross validation - it is a resampling version of the splitting into training-tuning-final model validation (aka test) method.

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