相关论文: Bayesian Variable Selection for Linear Regression …
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…
Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…
In linear regression models, fusion of coefficients is used to identify predictors having similar relationships with a response. This is called variable fusion. This paper presents a novel variable fusion method in terms of Bayesian linear…
In this article, we propose new Bayesian methods for selecting and estimating a sparse coefficient vector for skewed heteroscedastic response. Our novel Bayesian procedures effectively estimate the median and other quantile functions,…
This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…
Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent…
Consider a set of categorical variables where at least one of them is binary. The log-linear model that describes the counts in the resulting contingency table implies a specific logistic regression model, with the binary variable as the…
We consider Bayesian variable selection in sparse high-dimensional regression, where the number of covariates $p$ may be large relative to the samples size $n$, but at most a moderate number $q$ of covariates are active. Specifically, we…
We consider a Gaussian sequence space model $X_{\lambda}=f_{\lambda} + \xi_{\lambda},$ where $\xi $ has a diagonal covariance matrix $\Sigma=\diag(\sigma_\lambda ^2)$. We consider the situation where the parameter vector $(f_{\lambda})$ is…
Selecting informative nodes over large-scale networks becomes increasingly important in many research areas. Most existing methods focus on the local network structure and incur heavy computational costs for the large-scale problem. In this…
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,…
In the present work, we consider variable selection and shrinkage for the Gaussian dynamic linear regression within a Bayesian framework. In particular, we propose a novel method that allows for time-varying sparsity, based on an extension…
We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…
We consider Bayesian variable selection for binary outcomes under a probit link with a spike-and-slab prior on the regression coefficients. Motivated by the computational challenges encountered by Markov chain Monte Carlo (MCMC) samplers in…
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…
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…
Bayesian methods are increasingly applied in these days in the theory and practice of statistics. Any Bayesian inference depends on a likelihood and a prior. Ideally one would like to elicit a prior from related sources of information or…