Oracle Inequalities for a Group Lasso Procedure Applied to Generalized Linear Models in High Dimension
Oracle Inequalities for a Group Lasso Procedure Applied to Generalized Linear Models in High Dimension
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DOI：
10.1109/tit.2014.2303121
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发表时间：
2014-04-01
影响因子：
2.5
通讯作者：
Gamboa, Fabrice
中科院分区：
文献类型：
--
作者：
Blazere, Melanie;Loubes, Jean-Michel;Gamboa, Fabrice
给出了广义线性模型的一个组LASSO过程，并研究了该估计量应用于稀疏高维广义线性模型的性质。在协变量和协变量联合分布的一般条件下，给出了提升协变量组稀疏性的Oracle不等式。我们得到了预测和估计误差的收敛速度，并证明了该估计量能够恢复真实模型的良好稀疏逼近。然后，我们将这一过程推广到弹性净罚金的情况。最后，我们将这些结果应用于所谓的泊松回归模型(输出被建模为泊松过程，其强度依赖于协变量的线性组合)。组套索方法使得能够从输入集合中选择几组有意义的变量。
We present a group lasso procedure for generalized linear models (GLMs) and we study the properties of this estimator applied to sparse high-dimensional GLMs. Under general conditions on the covariates and on the joint distribution of the pair covariates, we provide oracle inequalities promoting group sparsity of the covariables. We get convergence rates for the prediction and estimation error and we show the ability of this estimator to recover good sparse approximation of the true model. Then, we extend this procedure to the case of an elastic net penalty. At last, we apply these results to the so-called Poisson regression model (the output is modeled as a Poisson process whose intensity relies on a linear combination of the covariables). The group lasso method enables to select few groups of meaningful variables among the set of inputs.