极小化非光滑惩罚目标函数的MM算法
MM Algorithms for Minimizing Nonsmoothly Penalized Objective Functions
摘要：
在本文中，我们提出了一个通用类的算法优化各种各样的非光滑惩罚的目标函数，满足一定的正则条件。该框架利用优化最小化（MM）算法作为其核心优化引擎。由此产生的算法依赖于迭代软阈值，实现组件，允许快速，稳定的更新，避免了任何高维矩阵求逆的需要。我们建立了一个局部收敛理论，这类算法在较弱的假设下比以前考虑的统计文献。我们还证明了新的加速方法，最初提出的期望最大化算法，在这类问题的特殊有效性。仿真结果和一个微阵列数据的例子来证明该算法的能力和通用性。
英文摘要：
In this paper, we propose a general class of algorithms for optimizing an extensive variety of nonsmoothly penalized objective functions that satisfy certain regularity conditions. The proposed framework utilizes the majorization-minimization (MM) algorithm as its core optimization engine. The resulting algorithms rely on iterated soft-thresholding, implemented componentwise, allowing for fast, stable updating that avoids the need for any high-dimensional matrix inversion. We establish a local convergence theory for this class of algorithms under weaker assumptions than previously considered in the statistical literature. We also demonstrate the exceptional effectiveness of new acceleration methods, originally proposed for the EM algorithm, in this class of problems. Simulation results and a microarray data example are provided to demonstrate the algorithm's capabilities and versatility.
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