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Split LBI: An Iterative Regularization Path with Structural Sparsity
Chendi Huang · Xinwei Sun · Jiechao Xiong · Yuan Yao

Wed Dec 07 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #77 #None
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.

Author Information

Chendi Huang (Peking University)
Xinwei Sun (Peking University)
Jiechao Xiong (Peking University)
Yuan Yao (Stanford University)

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