English
Related papers

Related papers: Bayesian Model Selection via Mean-Field Variationa…

200 papers

Recent progress in deep latent variable models has largely been driven by the development of flexible and scalable variational inference methods. Variational training of this type involves maximizing a lower bound on the log-likelihood,…

Machine Learning · Computer Science 2016-06-02 Andriy Mnih , Danilo J. Rezende

Variational Bayes (VB) is a popular tool for Bayesian inference in statistical modeling. Recently, some VB algorithms are proposed to handle intractable likelihoods with applications such as approximate Bayesian computation. In this paper,…

Numerical Analysis · Mathematics 2021-09-28 Zhijian He , Zhenghang Xu , Xiaoqun Wang

The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from…

Statistics Theory · Mathematics 2017-12-27 Debdeep Pati , Anirban Bhattacharya , Yun Yang

Reconstructing the evolutionary history relating a collection of molecular sequences is the main subject of modern Bayesian phylogenetic inference. However, the commonly used Markov chain Monte Carlo methods can be inefficient due to the…

Machine Learning · Statistics 2024-08-12 Tianyu Xie , Frederick A. Matsen , Marc A. Suchard , Cheng Zhang

Explaining how overparametrized neural networks simultaneously achieve low risk and zero empirical risk on benchmark datasets is an open problem. PAC-Bayes bounds optimized using variational inference (VI) have been recently proposed as a…

Machine Learning · Computer Science 2020-03-06 Konstantinos Pitas

We provide a rigorous analysis of training by variational inference (VI) of Bayesian neural networks in the two-layer and infinite-width case. We consider a regression problem with a regularized evidence lower bound (ELBO) which is…

Machine Learning · Statistics 2023-07-12 Arnaud Descours , Tom Huix , Arnaud Guillin , Manon Michel , Éric Moulines , Boris Nectoux

Extreme mass ratio inspirals (EMRIs) are thought to be one of the most exciting gravitational wave sources to be detected with LISA. Due to their complicated nature and weak amplitudes the detection and parameter estimation of such sources…

General Relativity and Quantum Cosmology · Physics 2013-01-04 Asad Ali , Nelson Christensen , Renate Meyer , Christian Röver

We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The…

Machine Learning · Computer Science 2015-05-19 Dan Geiger , David Heckerman , Christopher Meek

Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model…

Machine Learning · Statistics 2018-10-30 Sébastien Marmin , Maurizio Filippone

Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs…

Methodology · Statistics 2026-03-03 Seunghyeon Kim , Kwangmin Lee , Yeonhee Park

In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are…

Information Theory · Computer Science 2017-04-05 Mihai-Alin Badiu , Thomas Lundgaard Hansen , Bernard Henri Fleury

Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that…

Methodology · Statistics 2022-11-22 Rafael Cabral , David Bolin , Håvard Rue

We develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods. Our main application is to the problem of mean-field variational inference, which…

Statistics Theory · Mathematics 2025-06-02 Yiheng Jiang , Sinho Chewi , Aram-Alexandre Pooladian

We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…

Statistics Theory · Mathematics 2022-02-14 Xiao Fang , Malay Ghosh

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

We explore the theoretical and numerical property of a fully Bayesian model selection method in sparse ultrahigh-dimensional settings, i.e., $p\gg n$, where $p$ is the number of covariates and $n$ is the sample size. Our method consists of…

Methodology · Statistics 2013-03-13 Zuofeng Shang , Ping Li

The major goal of this paper is to study the second order frequentist properties of the marginal posterior distribution of the parametric component in semiparametric Bayesian models, in particular, a second order semiparametric…

Statistics Theory · Mathematics 2015-03-17 Yun Yang , Guang Cheng , David B. Dunson

In conducting non-linear dimensionality reduction and feature learning, it is common to suppose that the data lie near a lower-dimensional manifold. A class of model-based approaches for such problems includes latent variables in an unknown…

Machine Learning · Statistics 2020-08-20 Deborshee Sen , Theodore Papamarkou , David Dunson

Variational approximation has been widely used in large-scale Bayesian inference recently, the simplest kind of which involves imposing a mean field assumption to approximate complicated latent structures. Despite the computational…

Statistics Theory · Mathematics 2019-05-21 Purnamrita Sarkar , Y. X. Rachel Wang , Soumendu Sundar Mukherjee

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