Challenges with data in the big-data era include (i) the dimension $p$ is
often larger than the sample size $n$ (ii) outliers or contaminated points are
frequently hidden and more difficult to detect. Challenge (i) renders most
conventional methods inapplicable. Thus, it attracts tremendous attention from
statistics, computer science, and bio-medical communities. Numerous penalized
regression methods have been introduced as modern methods for analyzing
high-dimensional data. Disproportionate attention has been paid to the
challenge (ii) though. Penalized regression methods can do their job very well
and are expected to handle the challenge (ii) simultaneously. Most of them,
however, can break down by a single outlier (or single adversary contaminated
point) as revealed in this article.
The latter systematically examines leading penalized regression methods in
the literature in terms of their robustness, provides quantitative assessment,
and reveals that most of them can break down by a single outlier. Consequently,
a novel robust penalized regression method based on the least sum of squares of
depth trimmed residuals is proposed and studied carefully. Experiments with
simulated and real data reveal that the newly proposed method can outperform
some leading competitors in estimation and prediction accuracy in the cases
considered.

大数据时代中的数据挑战包括：维度常常大于样本大小，异常值或污染点通常隐藏且更难检测。这篇论文系统地检查了文献中的主要惩罚回归方法，并提出了一种基于剪枝残差最小平方和的鲁棒惩罚回归方法，实验证明在估计和预测准确性方面胜过其他竞争对手。

高维数据的深度修剪残差罚最小二乘回归模型

Robust penalized least squares of depth trimmed residuals regression for  high-dimensional data

Penalized regression methods, such as $L_1$ regularization, are routinely
used in high-dimensional applications, and there is a rich literature on
optimality properties under sparsity assumptions. In the Bayesian paradigm,
sparsity is routinely induced through two-component mixture priors having a
probability mass at zero, but such priors encounter daunting computational
problems in high dimensions. This has motivated an amazing variety of
continuous shrinkage priors, which can be expressed as global-local scale
mixtures of Gaussians, facilitating computation. In sharp contrast to the
frequentist literature, little is known about the properties of such priors and
the convergence and concentration of the corresponding posterior distribution.
In this article, we propose a new class of Dirichlet--Laplace (DL) priors,
which possess optimal posterior concentration and lead to efficient posterior
computation exploiting results from normalized random measure theory. Finite
sample performance of Dirichlet--Laplace priors relative to alternatives is
assessed in simulated and real data examples.

通过引入一类新的 Dirichlet-Laplace 先验，文章探讨在 Bayesian 范例下连续收缩先验的特点及性质，并对使用该先验进行的后验计算进行了评估。