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@@ -25,13 +25,13 @@ the following basic penalties
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and the following more sophisticated penalties
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-[Elastic net](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.ElasticNet.html) versions of the above
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- Adaptive Lasso versions of the above (including multi-task, group and nuclear norm)
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-[Adaptive Lasso](http://users.stat.umn.edu/~zouxx019/Papers/adalasso.pdf) versions of the above (including multi-task, group and nuclear norm)
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- Folded concave penalties (FCP) such as [SCAD](https://fan.princeton.edu/papers/01/penlike.pdf) fit by applying the *local linear approximation* (LLA) algorithm to a "good enough" initializer such as the Lasso fit ([Zou and Li, 2008](http://www.personal.psu.edu/ril4/research/AOS0316.pdf); [Fan et al, 2014](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4295817/)). We also provide concave versions of the group Lasso, multi-task Lasso and nuclear norm that are not discussed in the original paper.
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The built in cross-validation functionality supports
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- faster path algorithms for convex loss functions (as in sklearn.linear_model.LassoCV)
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- faster path algorithms for convex penalties and adaptive lasso (e.g. as in [sklearn.linear_model.LassoCV](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html))
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- automatically generated tuning parameter path for any loss + penalty combination
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- custom evaluation metrics
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- custom selection rules such as the '1se' rule from the glmnet package
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# References
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Beck, A. and Teboulle, M., 2009. [A fast iterative shrinkage-thresholding algorithm for linear inverse problems](https://epubs.siam.org/doi/pdf/10.1137/080716542?casa_token=cjyK5OxcbSoAAAAA:lQOp0YAVKIOv2-vgGUd_YrnZC9VhbgWvZgj4UPbgfw8I7NV44K82vbIu0oz2-xAACBz9k0Lclw). SIAM journal on imaging sciences, 2(1), pp.183-202.
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Zou, H., 2006. [The adaptive lasso and its oracle properties](http://users.stat.umn.edu/~zouxx019/Papers/adalasso.pdf). Journal of the American statistical association, 101(476), pp.1418-1429.
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Zou, H. and Li, R., 2008. [One-step sparse estimates in nonconcave penalized likelihood models](http://www.personal.psu.edu/ril4/research/AOS0316.pdf). Annals of statistics, 36(4), p.1509.
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Beck, A. and Teboulle, M., 2009. [A fast iterative shrinkage-thresholding algorithm for linear inverse problems](https://epubs.siam.org/doi/pdf/10.1137/080716542?casa_token=cjyK5OxcbSoAAAAA:lQOp0YAVKIOv2-vgGUd_YrnZC9VhbgWvZgj4UPbgfw8I7NV44K82vbIu0oz2-xAACBz9k0Lclw). SIAM journal on imaging sciences, 2(1), pp.183-202.
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Fan, J., Xue, L. and Zou, H., 2014. [Strong oracle optimality of folded concave penalized estimation](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4295817/). Annals of statistics, 42(3), p.819.
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