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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…

Machine Learning · Statistics 2013-03-26 Rajarshi Guhaniyogi , David B. Dunson

We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…

Methodology · Statistics 2019-04-10 Antik Chakraborty , Anirban Bhattacharya , Bani K. Mallick

There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…

Computation · Statistics 2016-02-25 Xichen Huang , Jin Wang , Feng Liang

Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…

Methodology · Statistics 2023-10-10 Alexander C. McLain , Anja Zgodic , Howard Bondell

Recent works have shown an interest in investigating the frequentist asymptotic properties of Bayesian procedures for high-dimensional linear models under sparsity constraints. However, there exists a gap in the literature regarding…

Statistics Theory · Mathematics 2025-09-23 Marion Naveau , Maud Delattre , Laure Sansonnet

Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…

Statistics Theory · Mathematics 2024-09-18 Abhisek Chakraborty , Saptati Datta

Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…

Methodology · Statistics 2010-09-20 Anthony Lee , Francois Caron , Arnaud Doucet , Chris Holmes

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…

Methodology · Statistics 2014-07-09 Barbara E. Engelhardt , Ryan P. Adams

We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…

Machine Learning · Statistics 2016-04-21 Khai X. Chiong , Matthew Shum

We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…

Statistics Theory · Mathematics 2018-12-06 Ryan Martin , Raymond Mess , Stephen G. Walker

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

Machine Learning · Computer Science 2023-11-10 Anshuk Uppal , Kristoffer Stensbo-Smidt , Wouter Boomsma , Jes Frellsen

We consider full Bayesian inference in the multivariate normal mean model in the situation that the mean vector is sparse. The prior distribution on the vector of means is constructed hierarchically by first choosing a collection of nonzero…

Statistics Theory · Mathematics 2012-11-07 Ismaël Castillo , Aad van der Vaart

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…

Methodology · Statistics 2017-11-06 Zemei Xu , Daniel F. Schmidt , Enes Makalic , Guoqi Qian , John L. Hopper

We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing tail,…

Statistics Theory · Mathematics 2020-09-01 Kyoungjae Lee , Minwoo Chae , Lizhen Lin

We propose a new approach to Bayesian prediction that caters for models with a large number of parameters and is robust to model misspecification. Given a class of high-dimensional (but parametric) predictive models, this new approach…

Methodology · Statistics 2022-05-13 David T. Frazier , Ruben Loaiza-Maya , Gael M. Martin , Bonsoo Koo

We develop a Bayesian vector autoregressive (VAR) model with multivariate stochastic volatility that is capable of handling vast dimensional information sets. Three features are introduced to permit reliable estimation of the model. First,…

Computation · Statistics 2020-03-12 Gregor Kastner , Florian Huber

Random projection is often used to project higher-dimensional vectors onto a lower-dimensional space, while approximately preserving their pairwise distances. It has emerged as a powerful tool in various data processing tasks and has…

Machine Learning · Computer Science 2020-06-30 Wenye Li , Shuzhong Zhang

We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide approximate conjugacy in the model, the likelihood is approximated by a quadratic function, yielding…

Methodology · Statistics 2026-02-06 Mitra Kharabati , Morteza Amini , Mohammad Arashi

In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity,…

Methodology · Statistics 2022-07-04 Chang Liu , Yue Yang , Howard Bondell , Ryan Martin

Count data is prevalent in various fields like ecology, medical research, and genomics. In high-dimensional settings, where the number of features exceeds the sample size, feature selection becomes essential. While frequentist methods like…

Methodology · Statistics 2024-10-22 The Tien Mai