论文标题
支持稀疏关键估计的恢复和SUP-NORM收敛速率
Support recovery and sup-norm convergence rates for sparse pivotal estimation
论文作者
论文摘要
在高维稀疏回归中，关键估计器是最佳正则参数独立于噪声水平的估计器。规范的关键估计器是平方根的套索，及其衍生物作为“非平滑 +非平滑平滑”优化问题。解决这些问题的现代技术包括平滑数据拟合术语，从而受益于快速有效的近端算法。在这项工作中，我们显示了非平滑和平滑，单个任务和多任务平方根套索估计器的最小值sup-norm收敛速率。多亏了我们的理论分析，我们提供了一些有关如何设置平滑体参数的指南，并在合成数据上说明了此类准则的兴趣。
In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its derivatives as a "non-smooth + non-smooth" optimization problem. Modern techniques to solve these include smoothing the datafitting term, to benefit from fast efficient proximal algorithms. In this work we show minimax sup-norm convergence rates for non smoothed and smoothed, single task and multitask square-root Lasso-type estimators. Thanks to our theoretical analysis, we provide some guidelines on how to set the smoothing hyperparameter, and illustrate on synthetic data the interest of such guidelines.
