Related papers: Adaptive Hard Thresholding for Near-optimal Consis…
In this paper, we study the problem of sparse mean estimation under adversarial corruptions, where the goal is to estimate the $k$-sparse mean of a heavy-tailed distribution from samples contaminated by adversarial noise. Existing methods…
Cellwise outliers are likely to occur together with casewise outliers in modern data sets with relatively large dimension. Recent work has shown that traditional robust regression methods may fail for data sets in this paradigm. The…
We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known…
We study the problem of learning Bayesian networks where an $\epsilon$-fraction of the samples are adversarially corrupted. We focus on the fully-observable case where the underlying graph structure is known. In this work, we present the…
Among semiparametric regression models, partially linear additive models provide a useful tool to include additive nonparametric components as well as a parametric component, when explaining the relationship between the response and a set…
We study the problem of robustly estimating the mean of a $d$-dimensional distribution given $N$ examples, where most coordinates of every example may be missing and $\varepsilon N$ examples may be arbitrarily corrupted. Assuming each…
We study the robustness of conformal prediction, a powerful tool for uncertainty quantification, to label noise. Our analysis tackles both regression and classification problems, characterizing when and how it is possible to construct…
Adversarially robust learning aims to design algorithms that are robust to small adversarial perturbations on input variables. Beyond the existing studies on the predictive performance to adversarial samples, our goal is to understand…
This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear…
Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…
Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…
Machine learning and data analysis have been used in many robotics fields, especially for modelling. Data are usually the result of sensor measurements and, as such, they might be subjected to noise and outliers. The presence of outliers…
A robust estimator for a wide family of mixtures of linear regression is presented. Robustness is based on the joint adoption of the Cluster Weighted Model and of an estimator based on trimming and restrictions. The selected model provides…
The presence of data corruption in user-generated streaming data, such as social media, motivates a new fundamental problem that learns reliable regression coefficient when features are not accessible entirely at one time. Until now,…
High-dimensional linear regression is a fundamental tool in modern statistics, particularly when the number of predictors exceeds the sample size. The classical Lasso, which relies on the squared loss, performs well under Gaussian noise…
The task of robust linear estimation in the presence of outliers is of particular importance in signal processing, statistics and machine learning. Although the problem has been stated a few decades ago and solved using classical…
We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…
Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this paper, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a…
Heavy-tailed error distributions and predictors with anomalous values are ubiquitous in high-dimensional regression problems and can seriously jeopardize the validity of statistical analyses if not properly addressed. For more reliable…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…