相关论文: Jump-Diffusion Langevin Dynamics for Multimodal Po…

We extend the Langevin Monte Carlo (LMC) algorithm to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD). We show that (projected) LMC allows to sample in polynomial time from a…

We study numerical methods for sampling probability measures in high dimension where the underlying model is only approximately identified with a gradient system. Extended stochastic dynamical methods are discussed which have application to…

The Metropolis-Hastings method is often used to construct a Markov chain with a given $\pi$ as its stationary distribution. The method works even if $\pi$ is known only up to an intractable constant of proportionality. Polynomial time…

The Langevin Markov chain algorithms are widely deployed methods to sample from distributions in challenging high-dimensional and non-convex statistics and machine learning applications. Despite this, current bounds for the Langevin…

A canonical algorithm for log-concave sampling is the Langevin Algorithm, aka the Langevin Diffusion run with some discretization stepsize $\eta > 0$. This discretization leads the Langevin Algorithm to have a stationary distribution…

Stochastic gradient Langevin dynamics (SGLD) and stochastic gradient Hamiltonian Monte Carlo (SGHMC) are two popular Markov Chain Monte Carlo (MCMC) algorithms for Bayesian inference that can scale to large datasets, allowing to sample from…

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple…

The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…

Empirical Bayes provides a powerful approach to learning and adapting to latent structure in data. Theory and algorithms for empirical Bayes have a rich literature for sequence models, but are less understood in settings where latent…

Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo sampling algorithm for drawing samples from smooth probability densities over continuous spaces. We study the variant most widely used in practice, Metropolized…

Adaptive Langevin dynamics is a method for sampling the Boltzmann-Gibbs distribution at prescribed temperature in cases where the potential gradient is subject to stochastic perturbation of unknown magnitude. The method replaces the…

Latent position network models are a versatile tool in network science; applications include clustering entities, controlling for causal confounders, and defining priors over unobserved graphs. Estimating each node's latent position is…

Langevin MCMC gradient optimization is a class of increasingly popular methods for estimating a posterior distribution. This paper addresses the algorithm as applied in a decentralized setting, wherein data is distributed across a network…

Powerful ideas recently appeared in the literature are adjusted and combined to design improved samplers for Bayesian exponential random graph models. Different forms of adaptive Metropolis-Hastings proposals (vertical, horizontal and…

In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly…

It is known that gradient-based MCMC samplers for continuous spaces, such as Langevin Monte Carlo (LMC), can be derived as particle versions of a gradient flow that minimizes KL divergence on a Wasserstein manifold. The superior efficiency…

The Metropolis-adjusted Langevin algorithm (MALA) is a Metropolis-Hastings method for approximate sampling from continuous distributions. We derive upper bounds for the contraction rate in Kantorovich-Rubinstein-Wasserstein distance of the…

The Langevin sampling method relies on an accurate score matching while the existing massive multiple-input multiple output (MIMO) Langevin detection involves an inevitable singular value decomposition (SVD) to calculate the posterior…

Latent variable models are widely used in social and behavioural sciences, including education, psychology, and political science. With the increasing availability of large and complex datasets, high-dimensional latent variable models have…

Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invariant Langevin Dynamics (ALDI) or its extension using weighted…