Related papers: Adversarial robust weighted Huber regression
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 existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning…
Several recent results provide theoretical insights into the phenomena of adversarial examples. Existing results, however, are often limited due to a gap between the simplicity of the models studied and the complexity of those deployed in…
We study the task of noiseless linear regression under Gaussian covariates in the presence of additive oblivious contamination. Specifically, we are given i.i.d.\ samples from a distribution $(x, y)$ on $\mathbb{R}^d \times \mathbb{R}$ with…
We propose a class of robust estimates for multivariate linear models. Based on the approach of MM estimation (Yohai 1987), we estimate the regression coefficients and the covariance matrix of the errors simultaneously. These estimates have…
Adversarial examples have attracted significant attention in machine learning, but the reasons for their existence and pervasiveness remain unclear. We demonstrate that adversarial examples can be directly attributed to the presence of…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
Robust regression has attracted a great amount of attention in the literature recently, particularly for taking asymmetricity into account simultaneously and for high-dimensional analysis. However, the majority of research on the topics…
Decision making and learning in the presence of uncertainty has attracted significant attention in view of the increasing need to achieve robust and reliable operations. In the case where uncertainty stems from the presence of adversarial…
This paper is devoted to the problem of determining the concentration bounds that are achievable in non-parametric regression. We consider the setting where features are supported on a bounded subset of $\mathbb{R}^d$, the regression…
We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…
Why are classifiers in high dimension vulnerable to "adversarial" perturbations? We show that it is likely not due to information theoretic limitations, but rather it could be due to computational constraints. First we prove that, for a…
The inflated beta regression model is widely used for modeling continuous proportions with values at the boundaries. Maximum likelihood estimation for these models is well-known for its sensitivity to outliers, which can severely distort…
Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…
This paper analyzes $\ell_1$ regularized linear regression under the challenging scenario of having only adversarially corrupted data for training. We use the primal-dual witness paradigm to provide provable performance guarantees for the…
High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…
Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…
Considered here are robust subgroup-classifier learning and testing in change-plane regressions with heavy-tailed errors, which can identify subgroups as a basis for making optimal recommendations for individualized treatment. A new…
Network experiments are powerful tools for studying spillover effects, which avoid endogeneity by randomly assigning treatments to units over networks. However, it is non-trivial to analyze network experiments properly without imposing…
Despite achieving impressive performance, state-of-the-art classifiers remain highly vulnerable to small, imperceptible, adversarial perturbations. This vulnerability has proven empirically to be very intricate to address. In this paper, we…