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We analyze a recently proposed class of algorithms for the problem of sampling from probability distributions $\mu^\ast$ in $\mathbb{R}^d$ with a Lebesgue density of the form $\mu^\ast(x) \propto \exp(-f(Kx)-g(x))$, where $K$ is a linear…

Optimization and Control · Mathematics 2024-11-06 Martin Burger , Matthias J. Ehrhardt , Lorenz Kuger , Lukas Weigand

In this article we consider sampling from log concave distributions in Hamiltonian setting, without assuming that the objective gradient is globally Lipschitz. We propose two algorithms based on monotone polygonal (tamed) Euler schemes, to…

Probability · Mathematics 2023-01-20 Tim Johnston , Iosif Lytras , Sotirios Sabanis

Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…

Methodology · Statistics 2014-05-13 Tianqi Chen , Emily B. Fox , Carlos Guestrin

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…

Machine Learning · Computer Science 2018-12-03 Rong Ge , Holden Lee , Andrej Risteski

We study the Riemannian Langevin Algorithm for the problem of sampling from a distribution with density $\nu$ with respect to the natural measure on a manifold with metric $g$. We assume that the target density satisfies a log-Sobolev…

Machine Learning · Computer Science 2022-04-25 Khashayar Gatmiry , Santosh S. Vempala

Algorithms based on discretizing Langevin diffusion are popular tools for sampling from high-dimensional distributions. We develop novel connections between such Monte Carlo algorithms, the theory of Wasserstein gradient flow, and the…

Computation · Statistics 2019-05-13 Espen Bernton

We consider a family of unadjusted generalized HMC samplers, which includes standard position HMC samplers and discretizations of the underdamped Langevin process. A detailed analysis and optimization of the parameters is conducted in the…

Probability · Mathematics 2024-05-24 Nicolaï Gouraud , Pierre Le Bris , Adrien Majka , Pierre Monmarché

The Underdamped Langevin Monte Carlo (ULMC) is a popular Markov chain Monte Carlo sampling method. It requires the computation of the full gradient of the log-density at each iteration, an expensive operation if the dimension of the problem…

Machine Learning · Statistics 2020-10-23 Zhiyan Ding , Qin Li , Jianfeng Lu , Stephen J. Wright

Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm,…

Computation · Statistics 2016-04-20 Francois Septier , Gareth W. Peters

Langevin Dynamics has been extensively employed in global non-convex optimization due to the concentration of its stationary distribution around the global minimum of the potential function at low temperatures. In this paper, we propose to…

Optimization and Control · Mathematics 2023-05-22 Ryo Fujino

Sampling from a lattice Gaussian distribution is emerging as an important problem in various areas such as coding and cryptography. The default sampling algorithm --- Klein's algorithm yields a distribution close to the lattice Gaussian…

Information Theory · Computer Science 2016-11-18 Zheng Wang , Cong Ling , Guillaume Hanrot

In this paper, we analyse a proximal method based on the idea of forward-backward splitting for sampling from distributions with densities that are not necessarily smooth. In particular, we study the non-asymptotic properties of the…

Numerical Analysis · Mathematics 2022-01-25 Armin Eftekhari , Luis Vargas , Konstantinos Zygalakis

We propose a Markov chain Monte Carlo (MCMC) algorithm based on third-order Langevin dynamics for sampling from distributions with log-concave and smooth densities. The higher-order dynamics allow for more flexible discretization schemes,…

Machine Learning · Statistics 2020-05-27 Wenlong Mou , Yi-An Ma , Martin J. Wainwright , Peter L. Bartlett , Michael I. Jordan

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…

Machine Learning · Computer Science 2025-02-11 Emanuel Sommer , Jakob Robnik , Giorgi Nozadze , Uros Seljak , David Rügamer

In this article we consider static Bayesian parameter estimation for partially observed diffusions that are discretely observed. We work under the assumption that one must resort to discretizing the underlying diffusion process, for…

Computation · Statistics 2017-01-23 Ajay Jasra , Kengo Kamatani , Kody J. H. Law , Yan Zhou

We study a sequential Monte Carlo algorithm to sample from the Gibbs measure with a non-convex energy function at a low temperature. We use the practical and popular geometric annealing schedule, and use a Langevin diffusion at each…

Statistics Theory · Mathematics 2026-01-13 Ruiyu Han , Gautam Iyer , Dejan Slepčev

Error bounds are derived for sampling and estimation using a discretization of an intrinsically defined Langevin diffusion with invariant measure $\text{d}\mu_\phi \propto e^{-\phi} \mathrm{dvol}_g $ on a compact Riemannian manifold. Two…

Statistics Theory · Mathematics 2025-12-10 Karthik Bharath , Alexander Lewis , Akash Sharma , Michael V Tretyakov

We study Langevin-type algorithms for sampling from Gibbs distributions such that the potentials are dissipative and their weak gradients have finite moduli of continuity not necessarily convergent to zero. Our main result is a…

Statistics Theory · Mathematics 2024-03-01 Shogo Nakakita

We propose efficient Langevin Monte Carlo algorithms for sampling distributions with nonsmooth convex composite potentials, which is the sum of a continuously differentiable function and a possibly nonsmooth function. We devise such…

Machine Learning · Statistics 2022-07-12 Tim Tsz-Kit Lau , Han Liu

As an important Markov Chain Monte Carlo (MCMC) method, stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling. However, SGLD typically suffers from slow convergence…

Machine Learning · Computer Science 2019-11-05 Bao Wang , Difan Zou , Quanquan Gu , Stanley Osher