输出受到对抗性污染时基于Lasso的稳健估计

协方差矩阵的鲁棒估计：对抗污染及其他场景

Robust Estimation of Covariance Matrices: Adversarial Contamination and Beyond

针对高维低秩协方差矩阵估计中存在的对抗污染或重尾分布问题，提出一种自适应低秩结构与污染比例的鲁棒估计器，具备严格偏差保证，并给出高效数值近似算法。

Robust estimation of precision matrices under cellwise contamination

There is a great need for robust techniques in data mining and machine learning contexts where many standard techniques such as principal component analysis and linear discriminant analysis are inherently susceptible to outliers. Furthermore, standard robust procedures assume that less than half the observation rows of a data matrix are contaminated, which may not be a realistic assumption when the number of observed features is large. This work looks at the problem of estimating covariance and precision matrices under cellwise contamination. We consider using a robust pairwise covariance matr…

A New Sparse and Robust Adaptive Lasso Estimator for the Independent Contamination Model

Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted for. In past decades, the vast majority of robust linear regression estimators has focused on robustness against rowwise contamination. Even so called `high breakdown' estimators rely on the assumption that a majority of rows of the regression matrix is not affected by outliers. Only very recently, the first cellwise robust regression estimation methods hav…

A Robust Learning Algorithm for Regression Models Using Distributionally Robust Optimization under the Wasserstein Metric

We present a Distributionally Robust Optimization (DRO) approach to estimate a robustified regression plane in a linear regression setting, when the observed samples are potentially contaminated with adversarially corrupted outliers. Our approach mitigates the impact of outliers through hedging against a family of distributions on the observed data, some of which assign very low probabilities to the outliers. The set of distributions under consideration are close to the empirical distribution in the sense of the Wasserstein metric. We show that this DRO formulation can be relaxed to a convex o…

Evaluating Visual Properties via Robust HodgeRank

Nowadays, how to effectively evaluate visual properties has become a popular topic for fine-grained visual comprehension. In this paper we study the problem of how to estimate such visual properties from a ranking perspective with the help of the annotators from online crowdsourcing platforms. The main challenges of our task are two-fold. On one hand, the annotations often contain contaminated information, where a small fraction of label flips might ruin the global ranking of the whole dataset. On the other hand, considering the large data capacity, the annotations are often far from being com…

对抗鲁棒低秩矩阵估计：压缩感知与矩阵补全

Adversarial Robust Low Rank Matrix Estimation: Compressed Sensing and Matrix Completion

本文提出基于Huber损失与核范数惩罚的统一方法，解决对抗污染下的低秩矩阵估计，获得比以往更尖锐的误差界。

在重尾噪声下具有星形约束的鲁棒均值估计

Robust mean estimation under star-shaped constraints with heavy-tailed noise

研究在星形约束下对抗性污染数据的鲁棒均值估计问题，提出在有限二阶矩假设下，通过局部熵确定最小最大损失率，适用于已知或符号对称分布。

Statistical consistency and asymptotic normality for high-dimensional robust M-estimators

We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and covariates. We first establish a form of local statistical consistency for the penalized regression estimators under fairly mild conditions on the error distribution: When the derivative of the loss function is bounded and satisfies a local restricted curvature condition, all stationary points within a constant radius of the true regression vector converge at the m…

异常值稳健的稀疏/低秩最小二乘回归与稳健矩阵补全

Outlier-robust sparse/low-rank least-squares regression and robust matrix completion

本文在亚高斯框架下研究含对抗污染的高维稀疏/低秩回归与矩阵补全，提出基于排序Huber损失的易计算估计器，并证明其获得与污染比例和失败概率近最优且调参无需污染信息的估计速率。