Related papers: Universal Robust Regression via Maximum Mean Discr…

Consider the problem of simultaneous estimation of location and variance matrix under Huber's contaminated Gaussian model. First, we study minimum $f$-divergence estimation at the population level, corresponding to a generative adversarial…

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…

Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction…

Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on depth…

Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…

This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…

Fully robust versions of the elastic net estimator are introduced for linear and logistic regression. The algorithms to compute the estimators are based on the idea of repeatedly applying the non-robust classical estimators to data subsets…

This paper studies robust nonparametric regression, in which an adversarial attacker can modify the values of up to $q$ samples from a training dataset of size $N$. Our initial solution is an M-estimator based on Huber loss minimization.…

The Classical Tukey-Huber Contamination Model (CCM) is a usual framework to describe the mechanism of outliers generation in robust statistics. In a data set with $n$ observations and $p$ variables, under the CCM, an outlier is a unit, even…

We study the problem of robust mean estimation and introduce a novel Hamming distance-based measure of distribution shift for coordinate-level corruptions. We show that this measure yields adversary models that capture more realistic…

The last decade has seen a number of advances in computationally efficient algorithms for statistical methods subject to robustness constraints. An estimator may be robust in a number of different ways: to contamination of the dataset, to…

We study the problem of outlier robust high-dimensional mean estimation under a finite covariance assumption, and more broadly under finite low-degree moment assumptions. We consider a standard stability condition from the recent robust…

Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…

This paper proposes an adaptive penalized weighted mean regression for outlier detection of high-dimensional data. In comparison to existing approaches based on the mean shift model, the proposed estimators demonstrate robustness against…

Beta regression models are employed to model continuous response variables in the unit interval, like rates, percentages, or proportions. Their applications rise in several areas, such as medicine, environment research, finance, and natural…

In the classical contamination models, such as the gross-error (Huber and Tukey contamination model or Case-wise Contamination), observations are considered as the units to be identified as outliers or not. This model is very useful when…

Let $X$ be a random variable with unknown mean and finite variance. We present a new estimator of the mean of $X$ that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation…

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…