相关论文: Variational Bayes for high-dimensional linear regr…

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.…

Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been…

We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…

Heterogeneous, mixed type datasets including both continuous and categorical variables are ubiquitous, and enriches data analysis by allowing for more complex relationships and interactions to be modelled. Mixture models offer a flexible…

Recently, Stochastic Variational Inference (SVI) has been increasingly attractive thanks to its ability to find good posterior approximations of probabilistic models. It optimizes the variational objective with stochastic optimization,…

This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest…

We propose a variational Bayesian (VB) implementation of block-sparse Bayesian learning (BSBL) to compute proxy probability density functions (PDFs) that approximate the posterior PDFs of the weights and associated hyperparameters in a…

Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more…

Accurate tuning of hyperparameters is crucial to ensure that models can generalise effectively across different settings. In this paper, we present theoretical guarantees for hyperparameter selection using variational Bayes in the…

In this paper, we consider a Bayesian bi-level variable selection problem in high-dimensional regressions. In many practical situations, it is natural to assign group membership to each predictor. Examples include that genetic variants can…

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…

Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes the use of VB in many…

Variational inference is a fast and scalable alternative to Markov chain Monte Carlo and has been widely applied to posterior inference tasks in statistics and machine learning. A traditional approach for implementing mean-field variational…

Variational Bayes (VB) inference algorithm is used widely to estimate both the parameters and the unobserved hidden variables in generative statistical models. The algorithm -- inspired by variational methods used in computational physics…

While Bayesian methods are extremely popular in statistics and machine learning, their application to massive datasets is often challenging, when possible at all. Indeed, the classical MCMC algorithms are prohibitively slow when both the…

Variational Bayes (VB), a method originating from machine learning, enables fast and scalable estimation of complex probabilistic models. Thus far, applications of VB in discrete choice analysis have been limited to mixed logit models with…

Despite the popularism of Bayesian neural networks in recent years, its use is somewhat limited in complex and big data situations due to the computational cost associated with full posterior evaluations. Variational Bayes (VB) provides a…

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…

Sparse Bayesian Learning (SBL) is a powerful framework for attaining sparsity in probabilistic models. Herein, we propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) and show that, as its noise variance…