Sharp Oracle Inequalities for Stationary Points of Nonconvex Penalized M-Estimators
Sharp Oracle Inequalities for Stationary Points of Nonconvex Penalized M-Estimators
复制标题
非凸惩罚 M 估计量驻点的尖锐 Oracle 不等式
DOI：
10.1109/tit.2018.2863700
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发表时间：
2018
影响因子：
2.5
通讯作者：
Sara van de Geer
中科院分区：
文献类型：
--
作者：
A. Elsener;Sara van de Geer
许多统计估计程序导致非凸优化问题。解决这些问题的算法通常保证输出优化问题的稳定点。Oracle不等式是评价估计量统计性能的重要理论工具。Oracle的结果集中在不可计算的（全局）最小值或最大值的理论属性上。本文推广了一个用于凸优化问题导出驻点预言不等式的一般框架。这些预言不等式的一个主要的新成分是，它们是尖锐的：它们显示出接近模型内的最佳近似加上一个余项。我们将此框架应用于不同的估计问题。
Many statistical estimation procedures lead to nonconvex optimization problems. Algorithms to solve these problems are often guaranteed to output a stationary point of the optimization problem. Oracle inequalities are an important theoretical instrument to assess the statistical performance of an estimator. Oracle results have focused on the theoretical properties of the uncomputable (global) minimum or maximum. In this paper, a general framework used for convex optimization problems to derive oracle inequalities for stationary points is extended. A main new ingredient of these oracle inequalities is that they are sharp: they show closeness to the best approximation within the model plus a remainder term. We apply this framework to different estimation problems.
PUlasso：仅存在数据的高维变量选择
影响因子：
3.7
作者：
Song, Hyebin;Raskutti, Garvesh
通讯作者：
Raskutti, Garvesh