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We establish conditions under which Metropolis-Hastings (MH) algorithms with a position-dependent proposal covariance matrix will or will not have the geometric rate of convergence. Some of the diffusions based MH algorithms like the…

Methodology · Statistics 2022-08-23 Vivekananda Roy , Lijin Zhang

This paper proposes a new sampling scheme based on Langevin dynamics that is applicable within pseudo-marginal and particle Markov chain Monte Carlo algorithms. We investigate this algorithm's theoretical properties under standard…

Methodology · Statistics 2016-05-30 Christopher Nemeth , Chris Sherlock , Paul Fearnhead

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

Bayesian reasoning in linear mixed-effects models (LMMs) is challenging and often requires advanced sampling techniques like Markov chain Monte Carlo (MCMC). A common approach is to write the model in a probabilistic programming language…

Machine Learning · Computer Science 2025-03-25 Jinlin Lai , Justin Domke , Daniel Sheldon

Markov Chain Monte Carlo (MCMC) is one of the most powerful methods to sample from a given probability distribution, of which the Metropolis Adjusted Langevin Algorithm (MALA) is a variant wherein the gradient of the distribution is used…

Applications · Statistics 2022-01-21 Mariya Mamajiwala , Debasish Roy , Serge Guillas

The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…

Machine Learning · Statistics 2025-03-07 Zhiyan Ding , Qin Li

In this paper, we propose Barrier Hamiltonian Monte Carlo (BHMC), a version of the HMC algorithm which aims at sampling from a Gibbs distribution $\pi$ on a manifold $\mathrm{M}$, endowed with a Hessian metric $\mathfrak{g}$ derived from a…

Machine Learning · Statistics 2023-10-31 Maxence Noble , Valentin De Bortoli , Alain Durmus

Hamiltonian Monte Carlo (HMC) is a widely used sampler for continuous probability distributions. In many cases, the underlying Hamiltonian dynamics exhibit a phenomenon of resonance which decreases the efficiency of the algorithm and makes…

Computation · Statistics 2023-02-23 Lionel Riou-Durand , Pavel Sountsov , Jure Vogrinc , Charles C. Margossian , Sam Power

Along with the recent advances in scalable Markov Chain Monte Carlo methods, sampling techniques that are based on Langevin diffusions have started receiving increasing attention. These so called Langevin Monte Carlo (LMC) methods are based…

Computation · Statistics 2017-06-14 Umut Şimşekli

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…

Machine Learning · Computer Science 2024-03-12 Xunpeng Huang , Hanze Dong , Difan Zou , Tong Zhang

Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where…

Machine Learning · Computer Science 2019-09-13 Ruoqi Shen , Yin Tat Lee

We study the performance of an automated hybrid Monte Carlo (HMC) approach for conditional simulation of a recently proposed, single-parameter Gibbs Markov random field (Gibbs MRF). The MRF is based on a modified version of the planar…

Computational Physics · Physics 2020-07-08 Milan Žukovič , Dionissios T. Hristopulos

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…

Probability · Mathematics 2016-08-08 Sébastien Bubeck , Ronen Eldan , Joseph Lehec

This paper provides a convergence analysis for generalized Hamiltonian Monte Carlo samplers, a family of Markov Chain Monte Carlo methods based on leapfrog integration of Hamiltonian dynamics and kinetic Langevin diffusion, that encompasses…

Probability · Mathematics 2024-05-14 Evan Camrud , Alain Durmus , Pierre Monmarché , Gabriel Stoltz

We study the efficiency of Thompson sampling for contextual bandits. Existing Thompson sampling-based algorithms need to construct a Laplace approximation (i.e., a Gaussian distribution) of the posterior distribution, which is inefficient…

Machine Learning · Computer Science 2022-06-23 Pan Xu , Hongkai Zheng , Eric Mazumdar , Kamyar Azizzadenesheli , Anima Anandkumar

Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…

Probability · Mathematics 2018-12-27 Arnak S. Dalalyan , Lionel Riou-Durand

Sampling from distributions play a crucial role in aiding practitioners with statistical inference. However, in numerous situations, obtaining exact samples from complex distributions is infeasible. Consequently, researchers often turn to…

Computation · Statistics 2024-04-01 Riddhiman Bhattacharya , Tiefeng Jiang

Langevin diffusions are rapidly convergent under appropriate functional inequality assumptions. Hence, it is natural to expect that with additional smoothness conditions to handle the discretization errors, their discretizations like the…

Statistics Theory · Mathematics 2023-07-21 Alireza Mousavi-Hosseini , Tyler Farghly , Ye He , Krishnakumar Balasubramanian , Murat A. Erdogdu

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

In geostatistics, Gaussian random fields are often used to model heterogeneities of soil or subsurface parameters. To give spatial approximations of these random fields, they are discretized. Then, different techniques of geostatistical…

Computation · Statistics 2021-03-25 Sebastian Reuschen , Fabian Jobst , Wolfgang Nowak