We consider the problem of robustifying high-dimensional structured
estimation. Robust techniques are key in real-world applications which often
involve outliers and data corruption. We focus on trimmed versions of
structurally regularized M-estimators in the high-dimensional setting,
including the popular Least Trimmed Squares estimator, as well as analogous
estimators for generalized linear models and graphical models, using possibly
non-convex loss functions. We present a general analysis of their statistical
convergence rates and consistency, and then take a closer look at the trimmed
versions of the Lasso and Graphical Lasso estimators as special cases. On the
optimization side, we show how to extend algorithms for M-estimators to fit
trimmed variants and provide guarantees on their numerical convergence. The
generality and competitive performance of high-dimensional trimmed estimators
are illustrated numerically on both simulated and real-world genomics data.

研究如何在高维结构化估计中使用强鲁棒技术，包括利用非凸损失函数的修剪版本的结构化规则的 M 估计量，分析它们的统计收敛速率和一致性，并展示了其在基因组数据分析中的表现。

一类通用的修剪估计器族用于高维数据的稳健性分析

A General Family of Trimmed Estimators for Robust High-dimensional Data  Analysis

Web page ranking and collaborative filtering require the optimization of
sophisticated performance measures. Current Support Vector approaches are
unable to optimize them directly and focus on pairwise comparisons instead. We
present a new approach which allows direct optimization of the relevant loss
functions. This is achieved via structured estimation in Hilbert spaces. It is
most related to Max-Margin-Markov networks optimization of multivariate
performance measures. Key to our approach is that during training the ranking
problem can be viewed as a linear assignment problem, which can be solved by
the Hungarian Marriage algorithm. At test time, a sort operation is sufficient,
as our algorithm assigns a relevance score to every (document, query) pair.
Experiments show that the our algorithm is fast and that it works very well.

介绍了一种新的优化丢失功能的方法以提高 Web 页面排名和协同过滤的性能，并使用结构化估计在希尔伯特空间中进行直接优化，所提出的算法被证明是快速且表现良好。