Related papers: A majorization-minimization approach to variable s…

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…

Bayesian $l_0$-regularized least squares is a variable selection technique for high dimensional predictors. The challenge is optimizing a non-convex objective function via search over model space consisting of all possible predictor…

We consider Bayesian linear regression with sparsity-inducing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically…

Variable selection in the linear regression model takes many apparent faces from both frequentist and Bayesian standpoints. In this paper we introduce a variable selection method referred to as a rescaled spike and slab model. We study the…

In this paper we study grouped variable selection problems by proposing a specified prior, called the nested spike and slab prior, to model collective behavior of regression coefficients. At the group level, the nested spike and slab prior…

Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…

In the sparse normal means model, convergence of the Bayesian posterior distribution associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…

We study Bayesian group-regularized estimation in high-dimensional generalized linear models (GLMs) under a continuous spike-and-slab prior. Our framework covers both canonical and non-canonical link functions and subsumes logistic,…

Sample selection models are a widely used approach for correcting bias caused by data that are missing not at random. Their formulation requires specifying the variables that influence the outcome and those that drive the selection process.…

An important task in building regression models is to decide which regressors should be included in the final model. In a Bayesian approach, variable selection can be performed using mixture priors with a spike and a slab component for the…

We study the use of spike and slab priors for consistent estimation of the number of change points and their locations. Leveraging recent results in the variable selection literature, we show that an estimator based on spike and slab priors…

Rescaled spike and slab models are a new Bayesian variable selection method for linear regression models. In high dimensional orthogonal settings such models have been shown to possess optimal model selection properties. We review…

The impracticality of posterior sampling has prevented the widespread adoption of spike-and-slab priors in high-dimensional applications. To alleviate the computational burden, optimization strategies have been proposed that quickly find…

The paper revisits the Bayesian group lasso and uses spike and slab priors for group variable selection. In the process, the connection of our model with penalized regression is demonstrated, and the role of posterior median for…

There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…

We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized…

Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…

We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional…

Supervised topic models with a logistic likelihood have two issues that potentially limit their practical use: 1) response variables are usually over-weighted by document word counts; and 2) existing variational inference methods make…