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  "body": "\n## Summary\n\nThe elastic net fits a linear model by penalised least squares.\nIts penalty combines the $\\ell^1$ penalty of the [[lasso|KZ226116HW]] and the squared $\\ell^2$ penalty of [[ridge regression|3KZW2930V2]].\nIt keeps the variable selection of the lasso, since some coefficients are set exactly to zero.\nThe ridge part makes the problem strictly convex.\nIt also lets groups of strongly correlated regressors enter the model together, where the lasso tends to pick one of them.\nIt was proposed by Hui Zou and Trevor Hastie.\n\n## Explanations\n\n### L1 human\n\nThe lasso likes to keep one regressor out of a group of near copies and drop the rest.\nRidge regression keeps them all but never drops anything.\nThe elastic net mixes the two penalties with two tuning parameters, so it can drop useless regressors while sharing the weight among correlated useful ones.\nIf the ridge parameter is zero, it is the lasso; if the lasso parameter is zero, it is ridge regression.\n",
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