Related papers: Scalable Bayesian Learning with posteriors

Linear programming is widely used for decision-making in science, engineering, and operations research, yet in many modern applications the coefficients entering the constraints and objective are not known exactly and must be learned from…

The horseshoe prior is frequently employed in Bayesian analysis of high-dimensional models, and has been shown to achieve minimax optimal risk properties when the truth is sparse. While optimization-based algorithms for the extremely…

Solving Bayesian inverse problems typically involves deriving a posterior distribution using Bayes' rule, followed by sampling from this posterior for analysis. Sampling methods, such as general-purpose Markov chain Monte Carlo (MCMC), are…

We propose a novel adaptive empirical Bayesian method for sparse deep learning, where the sparsity is ensured via a class of self-adaptive spike-and-slab priors. The proposed method works by alternatively sampling from an adaptive…

The goal of Bayesian deep learning is to provide uncertainty quantification via the posterior distribution. However, exact inference over the weight space is computationally intractable due to the ultra-high dimensions of the neural…

Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…

This work proposes an adaptive sequential Monte Carlo sampling algorithm to solve Bayesian inverse problems in scenarios where likelihood evaluations are costly but can be approximated using a surrogate model built from previous evaluations…

Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…

Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social…

This article proposes a Bayesian approach to regression with a scalar response against vector and tensor covariates. Tensor covariates are commonly vectorized prior to analysis, failing to exploit the structure of the tensor, and resulting…

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…

The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…

For large model spaces, the potential entrapment of Markov chain Monte Carlo (MCMC) based methods with spike-and-slab priors poses significant challenges in posterior computation in regression models. On the other hand, maximum a posteriori…

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…

Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte…

Symbolic regression is a powerful tool for discovering governing equations directly from data, but its sensitivity to noise hinders its broader application. This paper introduces a Sequential Monte Carlo (SMC) framework for Bayesian…

Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…

Stochastic approximation Monte Carlo (SAMC) has recently been proposed by Liang, Liu and Carroll [J. Amer. Statist. Assoc. 102 (2007) 305--320] as a general simulation and optimization algorithm. In this paper, we propose to improve its…

The use of Cauchy Markov random field priors in statistical inverse problems can potentially lead to posterior distributions which are non-Gaussian, high-dimensional, multimodal and heavy-tailed. In order to use such priors successfully,…

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…