Outcomes of the equivalence of adaptive ridge with least absolute shrinkage
Proceedings of the 1998 conference on Advances in neural information processing systems II
The bias-variance tradeoff and the randomized GACV
Proceedings of the 1998 conference on Advances in neural information processing systems II
Penalized regression with correlation-based penalty
Statistics and Computing
Sparse hashing for fast multimedia search
ACM Transactions on Information Systems (TOIS)
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Lasso proved to be an extremely successful technique for simultaneous estimation and variable selection. However lasso has two major drawbacks. First, it does not enforce any grouping effect and secondly in some situation lasso solutions are inconsistent for variable selection. To overcome this inconsistency adaptive lasso is proposed where adaptive weights are used for penalizing different coefficients. Recently a doubly regularized technique namely elastic net is proposed which encourages grouping effect i.e. either selection or omission of the correlated variables together. However elastic net is also inconsistent. In this paper we study adaptive elastic net which does not have this drawback. In this article we specially focus on the grouped selection property of adaptive elastic net along with its model selection complexity. We also shed some light on the bias-variance tradeoff of different regularization methods including adaptive elastic net. An efficient algorithm was proposed in the line of LARS-EN, which is then illustrated with simulated as well as real life data examples.