Related papers: Spike-and-Slab Posterior Sampling in High Dimensio…
We introduce a symmetric random scan Gibbs sampler for scalable Bayesian variable selection that eliminates storage of the full cross-product matrix by computing required quantities on-the-fly. Data-informed proposal weights, constructed…
We consider the problem of sampling from the posterior distribution of a $d$-dimensional coefficient vector $\boldsymbol{\theta}$, given linear observations $\boldsymbol{y} = \boldsymbol{X}\boldsymbol{\theta}+\boldsymbol{\varepsilon}$. In…
Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…
Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of…
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 the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…
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…
Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…
Latent space models (LSMs) are frequently used to model network data by embedding a network's nodes into a low-dimensional latent space; however, choosing the dimension of this space remains a challenge. To this end, we begin by formalizing…
Sum-product networks (SPNs) are probabilistic models characterized by exact and fast evaluation of fundamental probabilistic operations. Its superior computational tractability has led to applications in many fields, such as machine…
This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and…
In this article, we propose a novel spatial global-local spike-and-slab selection prior for image-on-scalar regression. We consider a Bayesian hierarchical Gaussian process model for image smoothing, that uses a flexible Inverse-Wishart…
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…
Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…
In the present work, we consider variable selection and shrinkage for the Gaussian dynamic linear regression within a Bayesian framework. In particular, we propose a novel method that allows for time-varying sparsity, based on an extension…
Covariate-dependent graph learning has gained increasing interest in the graphical modeling literature for the analysis of heterogeneous data. This task, however, poses challenges to modeling, computational efficiency, and interpretability.…
Choosing between classical and Bayesian sparse regression methods involves a real trade-off: penalized estimators like Lasso run in milliseconds but give no uncertainty estimates,while Horseshoe and Spike-and-Slab priors produce full…
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.…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
Sparse regression based on global-local shrinkage priors are increasingly used for Bayesian modeling of modern high-dimensional data, but scaling up the Gibbs sampler for posterior inference remains a challenge. While much effort has gone…