Related papers: Robust Linear Regression for General Feature Distr…
We consider a robust estimation of linear regression coefficients. In this note, we focus on the case where the covariates are sampled from an $L$-subGaussian distribution with unknown covariance, the noises are sampled from a distribution…
The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…
We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…
Traditional methods for linear regression generally assume that the underlying error distribution, equivalently the distribution of the responses, is normal. Yet, sometimes real life response data may exhibit a skewed pattern, and assuming…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
Conformal prediction has received tremendous attention in recent years and has offered new solutions to problems in missing data and causal inference; yet these advances have not leveraged modern semiparametric efficiency theory for more…
We present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a…
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…
Supervised learning is all about the ability to generalize knowledge. Specifically, the goal of the learning is to train a classifier using training data, in such a way that it will be capable of classifying new unseen data correctly. In…
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…
Despite their numerous successes, there are many scenarios where adversarial risk metrics do not provide an appropriate measure of robustness. For example, test-time perturbations may occur in a probabilistic manner rather than being…
Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…
We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…
We provide a general framework for designing Generative Adversarial Networks (GANs) to solve high dimensional robust statistics problems, which aim at estimating unknown parameter of the true distribution given adversarially corrupted…
We study the problem of robust linear regression with response variable corruptions. We consider the oblivious adversary model, where the adversary corrupts a fraction of the responses in complete ignorance of the data. We provide a nearly…
We consider the robust linear regression problem in the online setting where we have access to the data in a streaming manner, one data point after the other. More specifically, for a true parameter $\theta^*$, we consider the corrupted…
We consider the question of Gaussian mean testing, a fundamental task in high-dimensional distribution testing and signal processing, subject to adversarial corruptions of the samples. We focus on the relative power of different…
The Gaussian cluster-weighted model (CWM) is a mixture of regression models with random covariates that allows for flexible clustering of a random vector composed of response variables and covariates. In each mixture component, it adopts a…
Constant (naive) imputation is still widely used in practice as this is a first easy-to-use technique to deal with missing data. Yet, this simple method could be expected to induce a large bias for prediction purposes, as the imputed input…
We study robust regression under a contamination model in which covariates are clean while the responses may be corrupted in an adaptive manner. Unlike the classical Huber's contamination model, where both covariates and responses may be…