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We study empirical Bayes estimation in high-dimensional linear regression. To facilitate computationally efficient estimation of the underlying prior, we adopt a variational empirical Bayes approach, introduced originally in Carbonetto and…

Statistics Theory · Mathematics 2023-10-27 Sumit Mukherjee , Bodhisattva Sen , Subhabrata Sen

Recently, a number of mostly $\ell_1$-norm regularized least squares type deterministic algorithms have been proposed to address the problem of \emph{sparse} adaptive signal estimation and system identification. From a Bayesian perspective,…

Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior…

Machine Learning · Statistics 2019-05-10 Artem Sobolev , Dmitry Vetrov

To address three important issues involved in latent variable models (LVMs), including capturing infrequent patterns, achieving small-sized but expressive models and alleviating overfitting, several studies have been devoted to…

Machine Learning · Computer Science 2017-11-27 Pengtao Xie , Jun Zhu , Eric P. Xing

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

Latent Gaussian models (LGMs) are a popular class of Bayesian hierarchical models that include Gaussian processes, as well as certain spatial models and mixed-effect models. Efficient Bayesian inference of LGMs often requires marginalizing…

Machine Learning · Statistics 2026-05-21 Jinlin Lai , Charles C. Margossian , Daniel R. Sheldon

Ordinary differential equations are arguably the most popular and useful mathematical tool for describing physical and biological processes in the real world. Often, these physical and biological processes are observed with errors, in which…

Methodology · Statistics 2016-07-26 Sarat C. Dass , Jaeyong Lee , Kyoungjae Lee , Jonghun Park

We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this it to reformulate the non-convex optimisation problem typically encountered in deep learning as a…

Machine Learning · Statistics 2023-10-24 Veit David Wild , Sahra Ghalebikesabi , Dino Sejdinovic , Jeremias Knoblauch

Variational Bayes (VB) is a common strategy for approximate Bayesian inference, but simple methods are only available for specific classes of models including, in particular, representations having conditionally conjugate constructions…

Methodology · Statistics 2019-11-19 Daniele Durante , Tommaso Rigon

Variational methods are attractive for computing Bayesian inference for highly parametrized models and large datasets where exact inference is impractical. They approximate a target distribution - either the posterior or an augmented…

Computation · Statistics 2019-11-21 Michael Stanley Smith , Ruben Loaiza-Maya , David J. Nott

Solving high-dimensional Bayesian inverse problems (BIPs) with the variational inference (VI) method is promising but still challenging. The main difficulties arise from two aspects. First, VI methods approximate the posterior distribution…

Numerical Analysis · Mathematics 2023-02-23 Yingzhi Xia , Qifeng Liao , Jinglai Li

While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…

Machine Learning · Statistics 2015-09-08 David A. Knowles

We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In…

Machine Learning · Statistics 2020-01-07 Prateek Jaiswal , Harsha Honnappa , Vinayak A. Rao

We propose a method to approximate the distribution of robot configurations satisfying multiple objectives. Our approach uses variational inference, a popular method in Bayesian computation, which has several advantages over sampling-based…

Robotics · Computer Science 2019-11-25 Emmanuel Pignat , Teguh Lembono , Sylvain Calinon

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…

Methodology · Statistics 2025-10-27 Kenyon Ng , Weichang Yu , Howard D. Bondell

Modern statistical applications involving large data sets have focused attention on statistical methodologies which are both efficient computationally and able to deal with the screening of large numbers of different candidate models. Here…

Methodology · Statistics 2014-02-26 David J. Nott , Minh-Ngoc Tran , Chenlei Leng

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…

Methodology · Statistics 2010-09-14 Chenlei Leng , Minh Ngoc Tran , David Nott

We define a novel class of additive models, called Extended Latent Gaussian Models, that allow for a wide range of response distributions and flexible relationships between the additive predictor and mean response. The new class covers a…

Methodology · Statistics 2022-07-13 Alex Stringer , Patrick Brown , Jamie Stafford

Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…

Methodology · Statistics 2024-07-31 Jay M. Ver Hoef , Eryn Blagg , Michael Dumelle , Philip M. Dixon , Dale L. Zimmerman , Paul Conn

Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to…

Machine Learning · Statistics 2018-02-22 Christian A. Naesseth , Scott W. Linderman , Rajesh Ranganath , David M. Blei