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A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and…

The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…

In this paper, we propose an abstract procedure for debiasing constrained or regularized potentially high-dimensional linear models. It is elementary to show that the proposed procedure can produce $\frac{1}{\sqrt{n}}$-confidence intervals…

In this paper, we develop connections between two seemingly disparate, but central, models in robust statistics: Huber's epsilon-contamination model and the heavy-tailed noise model. We provide conditions under which this connection…

This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of…

Microbial communities analysis is drawing growing attention due to the rapid development of high-throughput sequencing techniques nowadays. The observed data has the following typical characteristics: it is high-dimensional, compositional…

Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this…

Robust loss minimization is an important strategy for handling robust learning issue on noisy labels. Current approaches for designing robust losses involve the introduction of noise-robust factors, i.e., hyperparameters, to control the…

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently,…

The least-absolute shrinkage and selection operator (LASSO) is a regularization technique for estimating sparse signals of interest emerging in various applications and can be efficiently solved via the alternating direction method of…

In this paper we study how the choice of loss functions of non-convex optimization problems affects their robustness and optimization landscape, through the study of noisy matrix sensing. In traditional regression tasks, mean squared error…

We present a Distributionally Robust Optimization (DRO) approach to estimate a robustified regression plane in a linear regression setting, when the observed samples are potentially contaminated with adversarially corrupted outliers. Our…

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…

This study introduces a novel formulation to enhance Support Vector Machines (SVMs) in handling class imbalance and noise. Unlike the conventional Soft Margin SVM, which penalizes the magnitude of constraint violations, the proposed model…

It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…

Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…

We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to…

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…

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…

Real-world network applications must cope with failing nodes, malicious attacks, or nodes facing corrupted data - data classified as outliers. Our work addresses these concerns in the scope of the sensor network localization problem where,…