Related papers: R-VGAL: A Sequential Variational Bayes Algorithm f…

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

Linear mixed models are able to handle an extraordinary range of complications in regression-type analyses. Their most common use is to account for within-subject correlation in longitudinal data analysis. They are also the standard vehicle…

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 propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We…

Relevance Vector Machine (RVM) is a supervised learning algorithm extended from Support Vector Machine (SVM) based on the Bayesian sparsity model. Compared with the regression problem, RVM classification is difficult to be conducted because…

Large crossed mixed effects models with imbalanced structures and missing data pose major computational challenges for standard Bayesian posterior sampling algorithms, as the computational complexity is usually superlinear in the number of…

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…

Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such…

3D Gaussian Splatting (3DGS) has shown promising results for 3D scene modeling using mixtures of Gaussians, yet its existing simultaneous localization and mapping (SLAM) variants typically rely on direct, deterministic pose optimization…

Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core…

We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to…

Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately,…

We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general…

The R package spikeSlabGAM implements Bayesian variable selection, model choice, and regularized estimation in (geo-)additive mixed models for Gaussian, binomial, and Poisson responses. Its purpose is to (1) choose an appropriate subset of…

The learning and evaluation of energy-based latent variable models (EBLVMs) without any structural assumptions are highly challenging, because the true posteriors and the partition functions in such models are generally intractable. This…

Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…

Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…

We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…

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…

Moment-based estimation is a theoretically attractive approach to parametric inference, especially when likelihood-based estimation is unavailable, misspecified, or computationally inconvenient. However, the moment equations involve sample…