Related papers: High-Dimensional Robust Mean Estimation with Untru…

We consider high dimensional $M$-estimation in settings where the response $Y$ is possibly missing at random and the covariates $\mathbf{X} \in \mathbb{R}^p$ can be high dimensional compared to the sample size $n$. The parameter of interest…

This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…

We study the relationship between adversarial robustness and differential privacy in high-dimensional algorithmic statistics. We give the first black-box reduction from privacy to robustness which can produce private estimators with optimal…

This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate…

In this paper, we investigate the adversarial robustness of nonparametric regression, a fundamental problem in machine learning, under the setting where an adversary can arbitrarily corrupt a subset of the input data. While the robustness…

Nowadays, massive datasets are typically dispersed across multiple locations, encountering dual challenges of high dimensionality and huge sample size. Therefore, it is necessary to explore sufficient dimension reduction (SDR) methods for…

Distributionally Robust Optimization (DRO) provides a framework for decision-making under distributional uncertainty, yet its effectiveness can be compromised by outliers in the training data. This paper introduces a principled approach to…

Adversarial attack perturbs an image with an imperceptible noise, leading to incorrect model prediction. Recently, a few works showed inherent bias associated with such attack (robustness bias), where certain subgroups in a dataset (e.g.…

The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…

The US Census Bureau will deliberately corrupt data sets derived from the 2020 US Census, enhancing the privacy of respondents while potentially reducing the precision of economic analysis. To investigate whether this trade-off is…

This paper investigates testing for deviation of a high-dimensional mean vector $\boldsymbol{\mu}$. In contrast to the standard one-sample significance test of the form: $H_0^\texttt{e} : \boldsymbol{\mu} = \boldsymbol{\mu}_0$ versus…

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…

We study multivariate linear regression under Gaussian covariates in two settings, where data may be erased or corrupted by an adversary under a coordinate-wise budget. In the incomplete data setting, an adversary may inspect the dataset…

Convolutional neural network (CNN) has achieved unprecedented success in image super-resolution tasks in recent years. However, the network's performance depends on the distribution of the training sets and degrades on out-of-distribution…

We study the sublinear multivariate mean estimation problem in $d$-dimensional Euclidean space. Specifically, we aim to find the mean $\mu$ of a ground point set $A$, which minimizes the sum of squared Euclidean distances of the points in…

Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space. The asymptotic property of the sample MMD has…

We present a new finite-sample analysis of M-estimators of locations in $\mathbb{R}^d$ using the tool of the influence function. In particular, we show that the deviations of an M-estimator can be controlled thanks to its influence function…

We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…

We study the canonical statistical estimation problem of linear regression from $n$ i.i.d.~examples under $(\varepsilon,\delta)$-differential privacy when some response variables are adversarially corrupted. We propose a variant of the…

We study the fundamental task of outlier-robust mean estimation for heavy-tailed distributions in the presence of sparsity. Specifically, given a small number of corrupted samples from a high-dimensional heavy-tailed distribution whose mean…