The First-Order View of Boosting Methods: Computational Complexity and Connections to Regularization

author: Paul Grigas, Industrial Engineering and Operations Research Department, UC Berkeley
published: Aug. 26, 2013,   recorded: July 2013,   views: 3228


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Incremental Forward Stagewise Regression (FS") is a statistical algorithm that produces sparse coefficient profi les for linear regression. Using the tools of first-order methods in convex optimization, we analyze the computational complexity of FS" and its flexible variants with adaptive shrinkage parameters. We also show that a simple modi cation to FS" yields an O(1=k) convergent algorithm for the least squares LASSO t for any regularization parameter and any data-set | thereby quantitatively characterizing the nature of regularization implicitly induced by FS".

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