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Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This…

This study introduces Variational Automatic Relevance Determination (VARD), a novel approach tailored for fitting sparse additive regression models in high-dimensional settings. VARD distinguishes itself by its ability to independently…

This paper addresses the weak instruments problem in linear instrumental variable models from a Bayesian perspective. The new approach has two components. First, a novel predictor-dependent shrinkage prior is developed for the many…

Two-component mixture priors provide a traditional way to induce sparsity in high-dimensional Bayes models. However, several aspects of such a prior, including computational complexities in high-dimensions, interpretation of exact zeros and…

We propose a variational Bayesian (VB) procedure for high-dimensional linear model inferences with heavy tail shrinkage priors, such as student-t prior. Theoretically, we establish the consistency of the proposed VB method and prove that…

This study proposes a novel hierarchical prior for inferring possibly low-rank matrices measured with noise. We consider three-component matrix factorization, as in singular value decomposition, and its fully Bayesian inference. The…

We develop a Bayesian variable selection method, called SVEN, based on a hierarchical Gaussian linear model with priors placed on the regression coefficients as well as on the model space. Sparsity is achieved by using degenerate spike…

While inference-time scaling has significantly enhanced generative quality in large language and diffusion models, its application to vector-quantized (VQ) visual autoregressive modeling (VAR) remains unexplored. We introduce VAR-Scaling,…

Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…

Crossing of fitted conditional quantiles is a prevalent problem for quantile regression models. We propose a new Bayesian modelling framework that penalises multiple quantile regression functions toward the desired non-crossing space. We…

We reconcile the two worlds of dense and sparse modeling by exploiting the positive aspects of both. We employ a factor model and assume {the dynamic of the factors is non-pervasive while} the idiosyncratic term follows a sparse vector…

Variable selection remains a fundamental challenge in statistics, especially in nonparametric settings where model complexity can obscure interpretability. Bayesian tree ensembles, particularly the popular Bayesian additive regression trees…

As a special infinite-order vector autoregressive (VAR) model, the vector autoregressive moving average (VARMA) model can capture much richer temporal patterns than the widely used finite-order VAR model. However, its practicality has long…

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…

Deep learning's immense capabilities are often constrained by the complexity of its models, leading to an increasing demand for effective sparsification techniques. Bayesian sparsification for deep learning emerges as a crucial approach,…

Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…

We develop a Bayesian approach to estimate weight matrices in spatial autoregressive (or spatial lag) models. Datasets in regional economic literature are typically characterized by a limited number of time periods T relative to spatial…

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…

Variable selection in the linear regression model takes many apparent faces from both frequentist and Bayesian standpoints. In this paper we introduce a variable selection method referred to as a rescaled spike and slab model. We study the…

We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…