Related papers: Mean Field Approximation in Bayesian Variable Sele…

Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on…

Fast variational approximate algorithms are developed for Bayesian semiparametric regression when the response variable is a count, i.e. a non-negative integer. We treat both the Poisson and Negative Binomial families as models for the…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

In this paper we take up Bayesian inference in general multivariate stable distributions. We exploit the representation of Matsui and Takemura (2009) for univariate projections, and the representation of the distributions in terms of their…

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…

In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

Regression for spatially dependent outcomes poses many challenges, for inference and for computation. Non-spatial models and traditional spatial mixed-effects models each have their advantages and disadvantages, making it difficult for…

We consider a multivariate piecewise linear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured by the integrated mean square error. Multivariate piecewise linear interpolator is…

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…

Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model…

Statistical models often assume that data are generated near a structured, smooth, or low-dimensional set. A common approach is to use Bayesian latent variable models, in which each observation is associated with a latent coordinate on the…

Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…

While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…

This paper provides estimation and inference methods for an identified set's boundary (i.e., support function) where the selection among a very large number of covariates is based on modern regularized tools. I characterize the boundary…

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…

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…

Variational inference (VI) is a popular method for approximating intractable posterior distributions in Bayesian inference and probabilistic machine learning. In this paper, we introduce a general framework for quantifying the statistical…

We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a…

Few Bayesian methods for analyzing high-dimensional sparse survival data provide scalable variable selection, effect estimation and uncertainty quantification. Such methods often either sacrifice uncertainty quantification by computing…