Related papers: Tail-adaptive Bayesian shrinkage
Our goal is to develop a Bayesian model averaging technique in linear regression models that accommodates heavier tailed error densities than the normal distribution. Motivated by the use of the Huber loss function in the presence of…
Bayesian fused lasso is one of the sparse Bayesian methods, which shrinks both regression coefficients and their successive differences simultaneously. In this paper, we propose a Bayesian fused lasso modeling via horseshoe prior. By…
As a fundamental problem in machine learning and differential privacy (DP), DP linear regression has been extensively studied. However, most existing methods focus primarily on either regular data distributions or low-dimensional cases with…
Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…
High-dimensional vector autoregressive (VAR) models offer a versatile framework for multivariate time series analysis, yet face critical challenges from over-parameterization and uncertain lag order. In this paper, we systematically compare…
Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is…
This paper investigates asymptotic minimaxity properties of Bayesian multiple testing rules in the sparse Gaussian sequence model using a broad class of global-local scale mixtures of normals as priors for the means. Minimaxity is studied…
Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…
Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…
We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…
The paper presents an efficient method for simulating the tails of a target variable Z=h(X) which depends on a set of basic variables X=(X_1, ..., X_n). To this aim, variables X_i, i=1, ..., n are sequentially simulated in such a manner…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
In the present work, we consider variable selection and shrinkage for the Gaussian dynamic linear regression within a Bayesian framework. In particular, we propose a novel method that allows for time-varying sparsity, based on an extension…
Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations…
Substantial research on structured sparsity has contributed to analysis of many different applications. However, there have been few Bayesian procedures among this work. Here, we develop a Bayesian model for structured sparsity that uses a…
In the context of a vector autoregression (VAR) model, or any multivariate regression model, the number of relevant predictors may be small relative to the information set available from which to build a prediction equation. It is well…
This paper introduces a loss-based generalized Bayesian methodology for high-dimensional robust regression with serially correlated errors and predictors. The proposed framework employs a novel scaled pseudo-Huber (SPH) loss function, which…
In this paper, we propose a new Bayesian inference method for a high-dimensional sparse factor model that allows both the factor dimensionality and the sparse structure of the loading matrix to be inferred. The novelty is to introduce a…
We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing…