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Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…

We propose an algorithm for the efficient and robust sampling of the posterior probability distribution in Bayesian inference problems. The algorithm combines the local search capabilities of the Manifold Metropolis Adjusted Langevin…

Federated learning performed by a decentralized networks of agents is becoming increasingly important with the prevalence of embedded software on autonomous devices. Bayesian approaches to learning benefit from offering more information as…

In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…

Adaptive or dynamic signal sampling in sensing systems can adapt subsequent sampling strategies based on acquired signals, thereby potentially improving image quality and speed. This paper proposes a Bayesian method for adaptive sampling…

We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling…

Sampling from a high-dimensional distribution is a fundamental task in statistics, engineering, and the sciences. A canonical approach is the Langevin Algorithm, i.e., the Markov chain for the discretized Langevin Diffusion. This is the…

A key task in Bayesian statistics is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). However, without any assumptions, sampling (even approximately) can be #P-hard, and few…

A key task in Bayesian machine learning is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). One prevalent example of this is sampling posteriors in parametric distributions,…

We consider the problem of scalable sampling algorithms to fit Bayesian generalized linear mixed models on large datasets. Stochastic gradient Langevin dynamics, coupled with smooth re-parameterizations of variance parameters, produces…

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…

This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a…

In this paper, we examine the computational complexity of sampling from a Bayesian posterior (or pseudo-posterior) using the Metropolis-adjusted Langevin algorithm (MALA). MALA first employs a discrete-time Langevin SDE to propose a new…

Understanding the dimension dependency of computational complexity in high-dimensional sampling problem is a fundamental problem, both from a practical and theoretical perspective. Compared with samplers with unbiased stationary…

The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…

Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometry are included tend to have better performances, with the…

The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we…

Gradient-based Monte Carlo sampling algorithms, like Langevin dynamics and Hamiltonian Monte Carlo, are important methods for Bayesian inference. In large-scale settings, full-gradients are not affordable and thus stochastic gradients…

Markov chain Monte Carlo samplers based on discretizations of (overdamped) Langevin dynamics are commonly used in the Bayesian inference and computational statistical physics literature to estimate high-dimensional integrals. One can…