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This paper presents a detailed theoretical analysis of the Langevin Monte Carlo sampling algorithm recently introduced in Durmus et al. (Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau, 2016)…

Methodology · Statistics 2017-05-26 Nicolas Brosse , Alain Durmus , Éric Moulines , Marcelo Pereyra

Sampling from a log-concave distribution function is one core problem that has wide applications in Bayesian statistics and machine learning. While most gradient free methods have slow convergence rate, the Langevin Monte Carlo (LMC) that…

Machine Learning · Statistics 2020-10-23 Zhiyan Ding , Qin Li

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…

Numerical Analysis · Mathematics 2025-08-11 Tony Lelièvre , Régis Santet , Gabriel Stoltz

We study the problem of approximate sampling from non-log-concave distributions, e.g., Gaussian mixtures, which is often challenging even in low dimensions due to their multimodality. We focus on performing this task via Markov chain Monte…

Machine Learning · Statistics 2024-05-30 Tim Tsz-Kit Lau , Han Liu , Thomas Pock

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

We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely…

Computation · Statistics 2008-10-08 Y. Fan , D. S. Leslie , M. P. Wand

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 consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…

Computation · Statistics 2016-10-24 Richard A. Norton , J. Andres Christen , Colin Fox

Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…

Mathematical Finance · Quantitative Finance 2023-01-10 Michael B. Giles , Abdul-Lateef Haji-Ali

Field-level inference provides a means to optimally extract information from upcoming cosmological surveys, but requires efficient sampling of a high-dimensional parameter space. This work applies Microcanonical Langevin Monte Carlo (MCLMC)…

Cosmology and Nongalactic Astrophysics · Physics 2023-07-20 Adrian E. Bayer , Uros Seljak , Chirag Modi

Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, the canonical Euler-Maruyama discretization of the Langevin diffusion process, also named as Langevin Monte Carlo (LMC), studied…

Computation · Statistics 2020-10-06 Anh Duc Doan , Xin Dang , Dao Nguyen

We propose a novel sequential Monte Carlo (SMC) method for sampling from unnormalized target distributions based on a reverse denoising diffusion process. While recent diffusion-based samplers simulate the reverse diffusion using…

Computation · Statistics 2025-11-06 Luhuan Wu , Yi Han , Christian A. Naesseth , John P. Cunningham

Random sampling of graph partitions under constraints has become a popular tool for evaluating legislative redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed redistricting plan with an ensemble of sampled…

Applications · Statistics 2023-11-09 Cory McCartan , Kosuke Imai

We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…

Computation · Statistics 2019-10-15 Babak Shahbaba , Luis Martinez Lomeli , Tian Chen , Shiwei Lan

A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for good…

Statistics Theory · Mathematics 2011-11-11 Christian Schäfer , Nicolas Chopin

Self-learning Monte Carlo (SLMC) methods are recently proposed to accelerate Markov chain Monte Carlo (MCMC) methods using a machine learning model. With latent generative models, SLMC methods realize efficient Monte Carlo updates with less…

Machine Learning · Statistics 2023-09-21 Yuma Ichikawa , Akira Nakagawa , Hiromoto Masayuki , Yuhei Umeda

This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the Multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and…

Numerical Analysis · Mathematics 2014-12-23 Eike H. Mueller , Rob Scheichl , Tony Shardlow

We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate,…

Computation · Statistics 2015-09-14 Christian A. Naesseth , Fredrik Lindsten , Thomas B. Schön

We consider the outstanding problem of sampling from an unnormalized density that may be non-log-concave and multimodal. To enhance the performance of simple Markov chain Monte Carlo (MCMC) methods, techniques of annealing type have been…

Machine Learning · Statistics 2025-02-18 Wei Guo , Molei Tao , Yongxin Chen

Low-precision training has emerged as a promising low-cost technique to enhance the training efficiency of deep neural networks without sacrificing much accuracy. Its Bayesian counterpart can further provide uncertainty quantification and…

Machine Learning · Statistics 2024-07-16 Ziyi Wang , Yujie Chen , Qifan Song , Ruqi Zhang