This paper introduces a new regularized version of the robust
$\tau$-regression estimator for analyzing high-dimensional data sets subject to
gross contamination in the response variables and covariates. We call the
resulting estimator adaptive $\tau$-Lasso that is robust to outliers and
high-leverage points and simultaneously employs adaptive $\ell_1$-norm penalty
term to reduce the bias associated with large true regression coefficients.
More specifically, this adaptive $\ell_1$-norm penalty term assigns a weight to
each regression coefficient. For a fixed number of predictors $p$, we show that
the adaptive $\tau$-Lasso has the oracle property with respect to
variable-selection consistency and asymptotic normality for the regression
vector corresponding to the true support, assuming knowledge of the true
regression vector support. We then characterize its robustness via the
finite-sample breakdown point and the influence function. We carry-out
extensive simulations to compare the performance of the adaptive $\tau$-Lasso
estimator with that of other competing regularized estimators in terms of
prediction and variable selection accuracy in the presence of contamination
within the response vector/regression matrix and additive heavy-tailed noise.
We observe from our simulations that the class of $\tau$-Lasso estimators
exhibits robustness and reliable performance in both contaminated and
uncontaminated data settings, achieving the best or close-to-best for many
scenarios, except for oracle estimators. However, it is worth noting that no
particular estimator uniformly dominates others. We also validate our findings
on robustness properties through simulation experiments.

本文提出了一个新的正则化的自适应 tau-Lasso 估计器，用于分析响应变量和协变量受到强烈污染的高维数据集，能够同时使用自适应 L1 范数惩罚项降低大真实回归系数与降低偏差的关联性，具有良好的鲁棒性和可靠性，表现比同类估计器更好或接近最佳，特别是在污染数据和期望回归矩阵 / 响应向量的情况下。同时也在探索鲁棒性质方面进行了验证。

自适应 $τ$-Lasso: 其鲁棒性和 Oracle 特性

The Adaptive $τ$-Lasso: Its Robustness and Oracle Properties

Unsupervised learning of anomaly detection in high-dimensional data, such as
images, is a challenging problem recently subject to intense research. Through
careful modelling of the data distribution of normal samples, it is possible to
detect deviant samples, so called anomalies. Generative Adversarial Networks
(GANs) can model the highly complex, high-dimensional data distribution of
normal image samples, and have shown to be a suitable approach to the problem.
Previously published GAN-based anomaly detection methods often assume that
anomaly-free data is available for training. However, this assumption is not
valid in most real-life scenarios, a.k.a. in the wild. In this work, we
evaluate the effects of anomaly contaminations in the training data on
state-of-the-art GAN-based anomaly detection methods. As expected, detection
performance deteriorates. To address this performance drop, we propose to add
an additional encoder network already at training time and show that joint
generator-encoder training stratifies the latent space, mitigating the problem
with contaminated data. We show experimentally that the norm of a query image
in this stratified latent space becomes a highly significant cue to
discriminate anomalies from normal data. The proposed method achieves
state-of-the-art performance on CIFAR-10 as well as on a large, previously
untested dataset with cell images.

本研究提出一种使用生成对抗网络结合编码器进行无监督学习的异常检测方法，能够在污染数据的情况下识别图像中的异常，并在 CIFAR-10 数据集和一个未经测试的细胞图像数据集上实现了最先进的性能。

使用同时编码器训练从受污染的图像数据中无监督地学习异常检测

Unsupervised Learning of Anomaly Detection from Contaminated Image Data  using Simultaneous Encoder Training

We consider the dimensionality-reduction problem (finding a subspace
approximation of observed data) for contaminated data in the high dimensional
regime, where the number of observations is of the same magnitude as the number
of variables of each observation, and the data set contains some (arbitrarily)
corrupted observations. We propose a High-dimensional Robust Principal
Component Analysis (HR-PCA) algorithm that is tractable, robust to contaminated
points, and easily kernelizable. The resulting subspace has a bounded deviation
from the desired one, achieves maximal robustness -- a breakdown point of 50%
while all existing algorithms have a breakdown point of zero, and unlike
ordinary PCA algorithms, achieves optimality in the limit case where the
proportion of corrupted points goes to zero.

该研究探讨了高维数据降维中的异常值问题，提出了一种可应用核函数的高维稳健主成分分析算法，该算法最大化稳健性，并实现了在异常值比例为零时的最优结果。