Related papers: Scalable Bayesian shrinkage and uncertainty quanti…
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 propose a general framework using spike-and-slab prior distributions to aid with the development of high-dimensional Bayesian inference. Our framework allows inference with a general quasi-likelihood function. We show that highly…
The logistic regression model is the most popular model for analyzing binary data. In the absence of any prior information, an improper flat prior is often used for the regression coefficients in Bayesian logistic regression models. The…
We develop a fully Bayesian framework for function-on-scalars regression with many predictors. The functional data response is modeled nonparametrically using unknown basis functions, which produces a flexible and data-adaptive functional…
This work introduces a Bayesian methodology for fitting large discrete graphical models with spike-and-slab priors to encode sparsity. We consider a quasi-likelihood approach that enables node-wise parallel computation resulting in reduced…
P-splines provide a flexible setting for modeling nonlinear model components based on a discretized penalty structure with a relatively simple computational backbone. Under a Bayesian inferential framework based on Markov chain Monte Carlo,…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…
Exponential family models, generalized linear models (GLMs), generalized linear mixed models (GLMMs) and generalized additive models (GAMs) are widely used methods in statistics. However, many scientific applications necessitate constraints…
This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…
In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…
This paper adopts a Bayesian nonparametric mixture model where the mixing distribution belongs to the wide class of normalized homogeneous completely random measures. We propose a truncation method for the mixing distribution by discarding…
We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…
In various applications, we deal with high-dimensional positive-valued data that often exhibits sparsity. This paper develops a new class of continuous global-local shrinkage priors tailored to analyzing gamma-distributed observations where…
Robust Bayesian methods for high-dimensional regression problems under diverse sparse regimes are studied. Traditional shrinkage priors are primarily designed to detect a handful of signals from tens of thousands of predictors in the…
Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple…
High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands…
We introduce the spike-and-slab group lasso (SSGL) for Bayesian estimation and variable selection in linear regression with grouped variables. We further extend the SSGL to sparse generalized additive models (GAMs), thereby introducing the…
We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…
The PAC-Bayesian approach is a powerful set of techniques to derive non- asymptotic risk bounds for random estimators. The corresponding optimal distribution of estimators, usually called the Gibbs posterior, is unfortunately intractable.…