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--- data_analysis:shrinkage_methods [2020/04/09 06:37] – [6.2.2 The Lasso] prgram
+++ data_analysis:shrinkage_methods [2025/07/07 14:12] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
 ====== shrinkage methods ======
+[[blog:easy_lasso_logistic_regression]]
 [[https://www.stat.cmu.edu/~ryantibs/papers/bestsubset.pdf|best subset vs LASSO]]
+<<ELS>>
+subset selection
+  * discrete process : variables are either ratained or discarded
+  * often exhibits high variance, and so doesn't reduce the prediction error of the full model
+Shrinkage methods are more continuous, and don't suffer as much from high variability
 constrains or regularize
@@ Line 11: / Line 19: @@
 Again speaking roughly, unbiasedness는 수많은 parameters를 추정해야 하는 때에는 unaffordable luxury가 될 수 있음
 ~James-Stein Estimator
 =====6.2.1 Ridge Regression =====
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 ridge : s.t. $ \sum \beta_j^2 \leq s $
 lasso : s.t. $ \sum |\beta_j| \leq s $
-( $ \lambda $ 에 대해 s가 존재 )
+( $ \lambda $ 에 대해 s가 존재, 1-1 correspondence )
 => ridge와 lasso 는 best subset의 풀기 힘든 문제를, 풀기 쉬운 문제로 대체한 계산 가능한 대안.
-{{:data_analysis:pasted:20200403-221625.png?300}}
+{{:data_analysis:pasted:20200409-171304.png}}
-https://godongyoung.github.io/%EB%A8%B8%EC%8B%A0%EB%9F%AC%EB%8B%9D/2018/02/07/ISL-Linear-Model-Selection-and-Regularization_ch6.html
+그림 출처 : ESL
+{{:data_analysis:pasted:20200403-221625.png?500}}
+[[https://godongyoung.github.io/%EB%A8%B8%EC%8B%A0%EB%9F%AC%EB%8B%9D/2018/02/07/ISL-Linear-Model-Selection-and-Regularization_ch6.html|그림출처]]
 변수가 2개일 때. 오차의 등고선(동일한 RSS)과 constraint function. $ \hat{\beta} $는 LSE.
@@ Line 93: / Line 103: @@
 Cross Validation
+※ elestic net penalty
+$ \lambda \sum (\alpha \beta_j^2 + (1-\alpha)|\beta_j|) $