With the abundance of high-dimensional data, sparse regularization techniques are very popular in practice because of the built-in sparsity of their corresponding estimators. However, the success of sparse methods heavily relies on the assumption of sparsity in the underlying model. For models where the sparsity assumption fails, the performance of these sparse methods can be unsatisfactory and misleading. In this article, we consider the perturbed linear model, where the signal is given by the sum of sparse and dense signals. We propose a new penalization-based method, called Gava, to tackle this kind of signal by making use of a graphical structure among model predictors. The proposed Gava method covers several existing methods as special cases. Our numerical examples and theoretical studies demonstrate the effectiveness of the proposed Gava for estimation and prediction.

中文翻译：

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通过在预测变量中加入图形结构来恢复稀疏和密集信号的总和

随着高维数据的丰富，稀疏正则化技术在实践中非常流行，因为它们对应的估计器具有内置的稀疏性。然而，稀疏方法的成功很大程度上依赖于底层模型中的稀疏性假设。对于稀疏假设失败的模型，这些稀疏方法的性能可能不令人满意且具有误导性。在本文中，我们考虑扰动线性模型，其中信号由稀疏和密集信号之和给出。我们提出了一种新的基于惩罚的方法，称为 Gava，通过利用模型预测变量之间的图形结构来处理这种信号。提出的 Gava 方法涵盖了几种现有方法作为特殊情况。