Related papers: Efficient MCMC Sampling for Bayesian Matrix Factor…

The computational complexity of MCMC methods for the exploration of complex probability measures is a challenging and important problem. A challenge of particular importance arises in Bayesian inverse problems where the target distribution…

In this paper, we present a method for computing the marginal likelihood, also known as the model likelihood or Bayesian evidence, from Markov Chain Monte Carlo (MCMC), or other sampled posterior distributions. In order to do this, one…

In sampling tasks, it is common for target distributions to be known up to a normalizing constant. However, in many situations, even evaluating the unnormalized distribution can be costly or infeasible. This issue arises in scenarios such…

We consider the problem of sampling from posterior distributions for Bayesian models where some parameters are restricted to be orthogonal matrices. Such matrices are sometimes used in neural networks models for reasons of regularization…

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models,…

Markov chain Monte Carlo (MCMC) allows one to generate dependent replicates from a posterior distribution for effectively any Bayesian hierarchical model. However, MCMC can produce a significant computational burden. This motivates us to…

Bayesian inference for factorial hidden Markov models is challenging due to the exponentially sized latent variable space. Standard Monte Carlo samplers can have difficulties effectively exploring the posterior landscape and are often…

There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…

The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…

Bayesian model selection enables comparison and ranking of conceptual subsurface models described by spatial prior models, according to the support provided by available geophysical data. Deep generative neural networks can efficiently…

In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors.…

In statistical analysis, Monte Carlo (MC) stands as a classical numerical integration method. When encountering challenging sample problem, Markov chain Monte Carlo (MCMC) is a commonly employed method. However, the MCMC estimator is biased…

Bayesian variable selection regression (BVSR) is able to jointly analyze genome-wide genetic datasets, but the slow computation via Markov chain Monte Carlo (MCMC) hampered its wide-spread usage. Here we present a novel iterative method to…

Embarrassingly parallel Markov Chain Monte Carlo (MCMC) exploits parallel computing to scale Bayesian inference to large datasets by using a two-step approach. First, MCMC is run in parallel on (sub)posteriors defined on data partitions.…

The problem of Bayesian reduced rank regression is considered in this paper. We propose, for the first time, to use Langevin Monte Carlo method in this problem. A spectral scaled Student prior distrbution is used to exploit the underlying…

Non-negative matrix factorization (NMF) is widely used in many applications for dimensionality reduction. Inferring an appropriate number of factors for NMF is a challenging problem, and several approaches based on information criteria or…

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…

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…

Bayesian deep learning counts on the quality of posterior distribution estimation. However, the posterior of deep neural networks is highly multi-modal in nature, with local modes exhibiting varying generalization performance. Given a…

Learning a Bayesian network (BN) from data can be useful for decision-making or discovering causal relationships. However, traditional methods often fail in modern applications, which exhibit a larger number of observed variables than data…