Related papers: Robust Bayesian Model Averaging for Linear Regress…

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…

We study the problem of linear regression where both covariates and responses are potentially (i) heavy-tailed and (ii) adversarially contaminated. Several computationally efficient estimators have been proposed for the simpler setting…

Model averaging is an alternative to model selection for dealing with model uncertainty, which is widely used and very valuable. However, most of the existing model averaging methods are proposed based on the least squares loss function,…

We propose a new family of error distributions for model-based quantile regression, which is constructed through a structured mixture of normal distributions. The construction enables fixing specific percentiles of the distribution while,…

Linear regression estimators are known to be sensitive to outliers, and one alternative to obtain a robust and efficient estimator of the regression parameter is to model the error with Student's $t$ distribution. In this article, we…

Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this…

Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called \textit{pseudo-hyperbolic…

In many large-scale inverse problems, such as computed tomography and image deblurring, characterization of sharp edges in the solution is desired. Within the Bayesian approach to inverse problems, edge-preservation is often achieved using…

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,…

The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…

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…

Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…

Robust Bayesian methods for high-dimensional regression problems under diverse sparse regimes are studied. Traditional shrinkage priors are primarily designed to detect a handful of signals from tens of thousands of predictors in the…

Anomaly detection is crucial in industrial applications for identifying rare and unseen patterns to ensure system reliability. Traditional models, trained on a single class of normal data, struggle with real-world distributions where normal…

We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…

Frequentist robust variable selection has been extensively investigated in high-dimensional regression. Despite success, developing the corresponding statistical inference procedures remains a challenging task. Recently, tackling this…

Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…

In this paper, we study the learning rate of generalized Bayes estimators in a general setting where the hypothesis class can be uncountable and have an irregular shape, the loss function can have heavy tails, and the optimal hypothesis may…

Long-tailed classification poses a challenge due to its heavy imbalance in class probabilities and tail-sensitivity risks with asymmetric misprediction costs. Recent attempts have used re-balancing loss and ensemble methods, but they are…

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…