In this paper the Generalized Lasso model of R. Tibshirani is extended to consider multidimensional features (or groups of features) à la Group Lasso, by substituting the ℓ norm of the regularizer by the ℓ norm. The resultant model is called Generalized Group Lasso (GenGL), and it contains as particular cases the already known Group Lasso and Group Fused Lasso (GFL), but also new models as the Graph-Guided Group Fused Lasso, or the trend filtering for multidimensional features. We show how to solve them efficiently combining FISTA iterations with the Proximal Operator of the corresponding regularizer, which we compute using a dual formulation. Moreover, GenGL makes possible to introduce a new approach to Group Total Variation, the regularizer of GFL, that results in a training much faster than that of previous methods.
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机译：在本文中，R。Tibshirani的广义Lasso模型被扩展为考虑正则化器的ℓ范数，从而将正则化器的ℓ范数考虑到多维特征（或特征组）或组Lasso。生成的模型称为通用组套索（GenGL），在特定情况下，它包含已知的组套索和组融合的套索（GFL），以及新模型，如图形引导的组融合的套索，或多维的趋势过滤特征。我们展示了如何有效地将FISTA迭代与相应正则化器的近邻运算符相结合来解决它们，我们使用对偶公式进行计算。此外，GenGL还可以为Group Total Variation（GFL的正则化器）引入一种新方法，该方法可以比以前的方法更快地进行训练。
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