Perspective maximum likelihood-type estimation via proximal decomposition
Perspective maximum likelihood-type estimation via proximal decomposition
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DOI：
10.1214/19-ejs1662
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发表时间：
2018-05
影响因子：
1.1
通讯作者：
P. Combettes;Christian L. Muller
中科院分区：
文献类型：
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作者：
P. Combettes;Christian L. Muller
我们引入了一个优化模型的最大似然型估计（M-估计），概括了一大类现有的统计模型，包括Huber的伴随M-估计，欧文的Huber/Berhu伴随估计，缩放套索，支持向量机回归和惩罚估计结构稀疏。该模型被称为透视M-估计，利用观察到的凸M-估计伴随规模以及各种正则化的透视功能的实例。这样的功能是服从邻近分析，这导致原则和可证明收敛的优化算法通过邻近分裂。使用基于对偶的几何方法，我们得到新的邻近算子的几个感兴趣的透视函数。合成和真实世界的数据的数值实验说明了所提出的框架的广泛适用性。
We introduce an optimization model for maximum likelihood-type estimation (M-estimation) that generalizes a large class of existing statistical models, including Huber's concomitant M-estimator, Owen's Huber/Berhu concomitant estimator, the scaled lasso, support vector machine regression, and penalized estimation with structured sparsity. The model, termed perspective M-estimation, leverages the observation that convex M-estimators with concomitant scale as well as various regularizers are instances of perspective functions. Such functions are amenable to proximal analysis, which leads to principled and provably convergent optimization algorithms via proximal splitting. Using a geometrical approach based on duality, we derive novel proximity operators for several perspective functions of interest. Numerical experiments on synthetic and real-world data illustrate the broad applicability of the proposed framework.