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Split LBI: An Iterative Regularization Path with Structural Sparsity

Chendi Huang · Xinwei Sun · Jiechao Xiong · Yuan Yao

Area 5+6+7+8 #77

Keywords: [ Convex Optimization ] [ Ranking and Preference Learning ] [ Sparsity and Feature Selection ] [ Model Selection and Structure Learning ]

Abstract: An iterative regularization path with structural sparsity is proposed in this paper based on variable splitting and the Linearized Bregman Iteration, hence called \emph{Split LBI}. Despite its simplicity, Split LBI outperforms the popular generalized Lasso in both theory and experiments. A theory of path consistency is presented that equipped with a proper early stopping, Split LBI may achieve model selection consistency under a family of Irrepresentable Conditions which can be weaker than the necessary and sufficient condition for generalized Lasso. Furthermore, some $\ell_2$ error bounds are also given at the minimax optimal rates. The utility and benefit of the algorithm are illustrated by applications on both traditional image denoising and a novel example on partial order ranking.

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