Lasso vs. adaptive Lasso

LASSO and adaptive LASSO are two different things, right? (To me, the penalties look different, but I’m just checking whether I miss something.)

When you generally speak about elastic net, is the special case LASSO or adaptive LASSO?

Which one does the glmnet package do, provided you choose alpha=1?

Adaptive LASSO works on milder conditions, right? Both have the oracle property in suitable data, right?

Answer

Brief answers to your questions:

  • Lasso and adaptive lasso are different. (Check Zou (2006) to see how adaptive lasso differs from standard lasso.)
  • Lasso is a special case of elastic net. (See Zou & Hastie (2005).)
    Adaptive lasso is not a special case of elastic net.
    Elastic net is not a special case of lasso or adaptive lasso.
  • Function glmnet in “glmnet” package in R performs lasso (not adaptive lasso) for alpha=1.
  • Does lasso work under milder conditions than adaptive lasso? I cannot answer this one (should check Zou (2006) for insights).
  • Only the adaptive lasso (but not lasso or elastic net) has the oracle property. (See Zou (2006).)

References:

Attribution
Source : Link , Question Author : Mr Validation , Answer Author : Richard Hardy

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