Related papers: Robust linear regression with broad distributions …

Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…

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…

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 consider outlier-robust and sparse estimation of linear regression coefficients, when the covariates and the noises are contaminated by adversarial outliers and noises are sampled from a heavy-tailed distribution. Our results present…

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…

Recent work has shown that Transformers can perform in-context learning for linear regression under restrictive assumptions, including i.i.d. data, Gaussian noise, and Gaussian regression coefficients. However, real-world data often violate…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

This work presents a novel and effective method for fitting multidimensional ellipsoids to scattered data in the contamination of noise and outliers. We approach the problem as a Bayesian parameter estimate process and maximize the…

We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…

We go through the many considerations involved in fitting a model to data, using as an example the fit of a straight line to a set of points in a two-dimensional plane. Standard weighted least-squares fitting is only appropriate when there…

This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…

Whole robustness is a nice property to have for statistical models. It implies that the impact of outliers gradually vanishes as they approach plus or minus infinity. So far, the Bayesian literature provides results that ensure whole…

Many scientific and engineering applications require fitting regression models that are nonlinear in the parameters. Advances in computer hardware and software in recent decades have made it easier to fit such models. Relative to fitting…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

Robust and sparse estimation of linear regression coefficients is investigated. The situation addressed by the present paper is that covariates and noises are sampled from heavy-tailed distributions, and the covariates and noises are…

In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…

This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson--Gaussian noise, and when there are additional outliers in the measured data. The…

Model mis-specification (e.g. the presence of outliers) is commonly encountered in astronomical analyses, often requiring the use of ad hoc algorithms which are sensitive to arbitrary thresholds (e.g. sigma-clipping). For any given dataset,…

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…

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…