Related papers: Model Based Screening Embedded Bayesian Variable S…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
A conventional Bayesian approach to prediction uses the posterior distribution to integrate out parameters in a density for unobserved data conditional on the observed data and parameters. When the true posterior is intractable, it is…
In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a…
Posterior sampling with the spike-and-slab prior [MB88], a popular multimodal distribution used to model uncertainty in variable selection, is considered the theoretical gold standard method for Bayesian sparse linear regression [CPS09,…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…
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…
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…
Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly…
This paper presents a novel variational inference framework for deriving a family of Bayesian sparse Gaussian process regression (SGPR) models whose approximations are variationally optimal with respect to the full-rank GPR model enriched…
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…
Estimation of the covariance matrix for high-dimensional multivariate datasets is a challenging and important problem in modern statistics. In this paper, we focus on high-dimensional Gaussian DAG models where sparsity is induced on the…
To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of…
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…
This paper introduces a novel Bayesian approach for variable selection in high-dimensional and potentially sparse regression settings. Our method replaces the indicator variables in the traditional spike and slab prior with continuous,…
In practical regression applications, multiple covariates are often measured, but not all may be associated with the response variable. Identifying and including only the relevant covariates in the model is crucial for improving prediction…
Simulation models of critical systems often have parameters that need to be calibrated using observed data. For expensive simulation models, calibration is done using an emulator of the simulation model built on simulation output at…
We introduce a Bayesian framework for mixed-type multivariate regression using continuous shrinkage priors. Our framework enables joint analysis of mixed continuous and discrete outcomes and facilitates variable selection from the $p$…
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…
Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is…
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…