群体稀疏下的不确定性量化
Uncertainty Quantification Under Group Sparsity
摘要：
在群体稀疏下，惩罚回归中的不确定性的量化是一个重要的开放问题。在高维尺度下，假设高斯误差模型和设计矩阵及真系数的温和条件，我们建立了一种改进的参数自举方法对群套索的渐近有效性.自举样本的模拟提供了对大组系数的同时推断。通过大量的数值比较，我们证明了我们的引导方法比流行的竞争对手表现得更好，突出了其实用性。将理论结果推广到其他块范数惩罚和亚高斯误差，进一步拓宽了潜在的应用。
英文摘要：
Quantifying the uncertainty in penalized regression under group sparsity is an important open question. We establish, under a high-dimensional scaling, the asymptotic validity of a modified parametric bootstrap method for the group lasso, assuming a Gaussian error model and mild conditions on the design matrix and the true coefficients. Simulation of bootstrap samples provides simultaneous inferences on large groups of coefficients. Through extensive numerical comparisons, we demonstrate that our bootstrap method performs much better than popular competitors, highlighting its practical utility. The theoretical result is generalized to other block norm penalization and sub-Gaussian errors, which further broadens the potential applications.
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