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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Elastic net regularization ： ウィキペディア英語版 Elastic net regularization In statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L1 and L2 penalties of the lasso and ridge methods. ==Specification== The elastic net method overcomes the limitations of the LASSO (least absolute shrinkage and selection operator) method which uses a penalty function based on :$\backslash |\backslash beta\backslash |\_1\; =\; \backslash textstyle\; \backslash sum\_^p\; |\backslash beta\_j|.$ Use of this penalty function has several limitations. For example, in the "large ''p'', small ''n''" case (high-dimensional data with few examples), the LASSO selects at most n variables before it saturates. Also if there is a group of highly correlated variables, then the LASSO tends to select one variable from a group and ignore the others. To overcome these limitations, the elastic net adds a quadratic part to the penalty ($\backslash |\backslash beta\backslash |^2$), which when used alone is ridge regression (known also as Tikhonov regularization). The estimates from the elastic net method are defined by : $\backslash hat\; =\; \backslash underset\{\backslash operatorname\{argmin\}\}\; (\backslash |\; y-X\; \backslash beta\; \backslash |^2\; +\; \backslash lambda\_2\; \backslash |\backslash beta\backslash |^2\; +\; \backslash lambda\_1\; \backslash |\backslash beta\backslash |\_1)\; .$ The quadratic penalty term makes the loss function strictly convex, and it therefore has a unique minimum. The elastic net method includes the LASSO and ridge regression: in other words, each of them is a special case where $\backslash lambda\_1\; =\; \backslash lambda,\; \backslash lambda\_2\; =\; 0$ or $\backslash lambda\_1\; =\; 0,\; \backslash lambda\_2\; =\; \backslash lambda$. Meanwhile, the naive version of elastic net method finds an estimator in a two-stage procedure : first for each fixed $\backslash lambda\_2$ it finds the ridge regression coefficients, and then does a LASSO type shrinkage. This kind of estimation incurs a double amount of shrinkage, which leads to increased bias and poor predictions. To improve the prediction performance, the authors rescale the coefficients of the naive version of elastic net by multiplying the estimated coefficients by $(1\; +\; \backslash lambda\_2)$.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Elastic net regularization」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.