Related papers: Mean-field Variational Bayes for Sparse Probit Reg…
Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…
Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…
The quantile varying coefficient (VC) model can flexibly capture dynamical patterns of regression coefficients. In addition, due to the quantile check loss function, it is robust against outliers and heavy-tailed distributions of the…
We introduce Group Spike-and-slab Variational Bayes (GSVB), a scalable method for group sparse regression. A fast co-ordinate ascent variational inference (CAVI) algorithm is developed for several common model families including Gaussian,…
We develop a Bayesian framework for variable selection in linear regression with autocorrelated errors, accommodating lagged covariates and autoregressive structures. This setting occurs in time series applications where responses depend on…
Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…
We introduce a flexible empirical Bayes approach for fitting Bayesian generalized linear models. Specifically, we adopt a novel mean-field variational inference (VI) method and the prior is estimated within the VI algorithm, making the…
Linear mixed effects models are widely used in statistical modelling. We consider a mixed effects model with Bayesian variable selection in the random effects using spike-and-slab priors and developed a variational Bayes inference scheme…
Identifying the active factors that have significant impacts on the output of the complex system is an important but challenging variable selection problem in computer experiments. In this paper, a Bayesian hierarchical Gaussian process…
Bayesian methods hold significant promise for improving the uncertainty quantification ability and robustness of deep neural network models. Recent research has seen the investigation of a number of approximate Bayesian inference methods…
Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single…
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…
Statistical inference methods are fundamentally important in machine learning. Most state-of-the-art inference algorithms are variants of Markov chain Monte Carlo (MCMC) or variational inference (VI). However, both methods struggle with…
In many contexts, there is interest in selecting the most important variables from a very large collection, commonly referred to as support recovery or variable, feature or subset selection. There is an enormous literature proposing a rich…
Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…
Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…
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…
We study the theoretical properties of a variational Bayes method in the Gaussian Process regression model. We consider the inducing variables method introduced by Titsias (2009a) and derive sufficient conditions for obtaining contraction…
Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have…
The spatial error model (SEM) is a type of simultaneous autoregressive (SAR) model for analysing spatially correlated data. Markov chain Monte Carlo (MCMC) is one of the most widely used Bayesian methods for estimating SEM, but it has…