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I would like to interprete the coefficients of a elastic net regression (i'm using function glmnet()$beta in R).

The coefficients of the elastic net regularized regression are considered as a "biased" coefficient because a L1/L2 penalty added during the calculation.

So my question is, can these biased coefficients represente the pratical significance between the predictors and the response variable? If they can't, how can i transforme these coefficients into a unbiased one?

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  • $\begingroup$ If you want unbiased estimates of coefficients, you shouldn't use regularization $\endgroup$ – kjetil b halvorsen May 14 '18 at 12:19
  • $\begingroup$ @kjetilbhalvorsen, Thanks for the answer! My aim is to quantify the impact of every predictor to the reponse variable, which means the result should be interpretable, then I chose the regression method. But as I have a very high dimension dataset, and some predictors are highly correlated, the elastic net regularization maybe is a good way. At the same time, my data comes from the medical domain, so we need to have a estimate which is the closest to the reality. Do you have any other suggestion for getting a unbiased estimates?? $\endgroup$ – kmjkpkj May 14 '18 at 13:26
  • $\begingroup$ Why do you think that unbiased estimators are "closest to reality"? If regularization helps to reduce variance, those regularized estimators could well be better! $\endgroup$ – kjetil b halvorsen May 14 '18 at 13:45
  • $\begingroup$ it might be helpful to look at the difference between an unbiased estimator and a low MSE estimator. I've written about it here and I know there are other places on this site that discuss it too. The basic idea is that probably you'd rather be close with your particular sample than correct when averaged over all possible samples $\endgroup$ – jld May 14 '18 at 15:21

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