ORACLE INEQUALITIES AND OPTIMAL INFERENCE UNDER GROUP SPARSITY
ORACLE INEQUALITIES AND OPTIMAL INFERENCE UNDER GROUP SPARSITY
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DOI：
10.1214/11-aos896
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发表时间：
2011-08-01
影响因子：
4.5
通讯作者：
Tsybakov, Alexandre B.
中科院分区：
文献类型：
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作者：
Lounici, Karim;Pontil, Massimiliano;Tsybakov, Alexandre B.
我们考虑在高斯噪声模型下估计稀疏线性回归向量β * 的问题，用于预测和模型选择。我们假设先验知识是可用的稀疏模式，即一组变量被划分成规定的组，其中只有少数是相关的估计过程中。这个组稀疏性假设建议我们考虑将Group Lasso方法作为估计beta* 的一种方法。我们建立了该估计量的预测误差和l（2）估计误差的预言不等式.这些界限下的限制特征值条件的设计矩阵。在更强的条件下，我们得到了混合（2，p）-模的估计误差的界，其中1
We consider the problem of estimating a sparse linear regression vector beta* under a Gaussian noise model, for the purpose of both prediction and model selection. We assume that prior knowledge is available on the sparsity pattern, namely the set of variables is partitioned into prescribed groups, only few of which are relevant in the estimation process. This group sparsity assumption suggests us to consider the Group Lasso method as a means to estimate beta*. We establish oracle inequalities for the prediction and l(2) estimation errors of this estimator. These bounds hold under a restricted eigenvalue condition on the design matrix. Under a stronger condition, we derive bounds for the estimation error for mixed (2, p)-norms with 1