论文标题
通过原始二次迭代同时选择最佳子集选择和尺寸缩小
Simultaneous Best Subset Selection and Dimension Reduction via Primal-Dual Iterations
论文作者
论文摘要
稀疏的等级回归是一种基本的统计学习方法。在当代文献中，估计通常被表达为一种非凸优化，通常在数值计算中产生局部最佳。然而，他们的理论分析始终集中在整体最佳距离上，从而导致统计保证和数值计算之间存在差异。在这项研究中，我们提供了一种新算法来解决该问题，并为算法解决方案建立了几乎最佳的速率。我们还证明，该算法通过多项式迭代数来实现估计。此外，我们提出了一个广义信息标准，以同时确保支持集恢复和等级估计的一致性。在提出的标准下，我们表明我们的算法可以以显着的概率来实现Oracle降低的等级估计。数值研究和在卵巢癌遗传数据中的应用证明了我们方法的有效性和可伸缩性。
Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet, their theoretical analysis is always centered on the global optimum, resulting in a discrepancy between the statistical guarantee and the numerical computation. In this research, we offer a new algorithm to address the problem and establish an almost optimal rate for the algorithmic solution. We also demonstrate that the algorithm achieves the estimation with a polynomial number of iterations. In addition, we present a generalized information criterion to simultaneously ensure the consistency of support set recovery and rank estimation. Under the proposed criterion, we show that our algorithm can achieve the oracle reduced rank estimation with a significant probability. The numerical studies and an application in the ovarian cancer genetic data demonstrate the effectiveness and scalability of our approach.
