Related papers: Model Based Screening Embedded Bayesian Variable S…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…
Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…
We study variable selection (also called support recovery) in high-dimensional sparse linear regression when one has external information on which variables are likely to be associated with the response. Consistent recovery is only possible…
In this work, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an…
Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…
We describe a numerical scheme for evaluating the posterior moments of Bayesian linear regression models with partial pooling of the coefficients. The principal analytical tool of the evaluation is a change of basis from coefficient space…
We address the problem of dynamic variable selection in time series regression with unknown residual variances, where the set of active predictors is allowed to evolve over time. To capture time-varying variable selection uncertainty, we…
Conjugate priors allow for fast inference in large dimensional vector autoregressive (VAR) models but, at the same time, introduce the restriction that each equation features the same set of explanatory variables. This paper proposes a…
Bounded continuous responses -- such as proportions -- arise frequently in diverse scientific fields including climatology, biostatistics, and finance. Beta regression is a widely adopted framework for modeling such data, due to the…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
We propose a robust and scalable framework for variational Bayes (VB) that effectively handles outliers and contamination of arbitrary nature in large datasets. Our approach divides the dataset into disjoint subsets, computes the posterior…
Many papers on high-dimensional statistics have proposed methods for variable selection and inference in linear regression models by relying explicitly or implicitly on the assumption that all regressors are exogenous. However, applications…
We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…
Double generalized linear models provide a flexible framework for modeling data by allowing the mean and the dispersion to vary across observations. Common members of the exponential dispersion family including the Gaussian, Poisson,…
In this article, we develop a distributed variable screening method for generalized linear models. This method is designed to handle situations where both the sample size and the number of covariates are large. Specifically, the proposed…
Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
We present a novel Bayesian approach for high-dimensional grouped regression under sparsity. We leverage a sparse projection method that uses a sparsity-inducing map to derive an induced posterior on a lower-dimensional parameter space. Our…
We present a generative modeling approach based on the variational inference framework for likelihood-free simulation-based inference. The method leverages latent variables within variational autoencoders to efficiently estimate complex…