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Langevin Monte Carlo (LMC) is a popular Bayesian sampling method. For the log-concave distribution function, the method converges exponentially fast, up to a controllable discretization error. However, the method requires the evaluation of…

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

We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…

Methodology · Statistics 2022-08-26 Paul B. Rohrbach , Robert L. Jack

In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…

Computation · Statistics 2025-01-23 Matthias J. Ehrhardt , Lorenz Kuger , Carola-Bibiane Schönlieb

The complex Langevin method is one hopeful candidate to tackle the sign problem. This method is applicable not only to QCD but also to nonrelativistic field theory, such as condensed matter physics. We present the simulation results of a…

High Energy Physics - Lattice · Physics 2015-08-04 Arata Yamamoto , Tomoya Hayata

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

We study sampling from a target distribution $\nu_* = e^{-f}$ using the unadjusted Langevin Monte Carlo (LMC) algorithm when the potential $f$ satisfies a strong dissipativity condition and it is first-order smooth with a Lipschitz…

Machine Learning · Statistics 2021-07-09 Murat A. Erdogdu , Rasa Hosseinzadeh , Matthew S. Zhang

QCD at nonzero baryon chemical potential suffers from the sign problem, due to the complex quark determinant. Complex Langevin dynamics can provide a solution, provided certain conditions are met. One of these conditions, holomorphicity of…

High Energy Physics - Lattice · Physics 2017-06-07 Gert Aarts , Erhard Seiler , Denes Sexty , Ion-Olimpiu Stamatescu

The complex Langevin (CL) method shows great promise in enabling the calculation of observables for theories with complex actions. Nevertheless, real-time quantum field theories have remained largely unsolved due to the particular severity…

High Energy Physics - Lattice · Physics 2024-01-12 Kirill Boguslavski , Paul Hotzy , David I. Müller

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 complex Langevin simulations, the insufficient decay of the probability density near infinity leads to boundary terms that spoil the formal argument for correctness. We present a formulation of this term that is cheaply measurable in…

High Energy Physics - Lattice · Physics 2021-12-07 Michael W. Hansen , Erhard Seiler , Dénes Sexty , Ion-Olimipu Stamatescu

Recent progress of the complex Langevin method and the Lefschetz thimble in connection with the sign problem is reviewed. These methods rely on the complexification of the original field manifold and they allow direct simulations of…

High Energy Physics - Lattice · Physics 2014-12-01 Denes Sexty

Markov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, whenever either the distribution does not exist in closed form, or, if it does, no efficient method to simulate an independent sample from…

Computation · Statistics 2008-07-22 Ioana A. Cosma , Masoud Asgharian

The problem of sampling a target probability distribution on a constrained domain arises in many applications including machine learning. For constrained sampling, various Langevin algorithms such as projected Langevin Monte Carlo (PLMC),…

Machine Learning · Statistics 2026-04-07 Yingli Wang , Changwei Tu , Xiaoyu Wang , Lingjiong Zhu

We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the…

Computation · Statistics 2016-07-04 Thomas Bonis

Classically, the continuous-time Langevin diffusion converges exponentially fast to its stationary distribution $\pi$ under the sole assumption that $\pi$ satisfies a Poincar\'e inequality. Using this fact to provide guarantees for the…

Statistics Theory · Mathematics 2024-07-11 Sinho Chewi , Murat A. Erdogdu , Mufan Bill Li , Ruoqi Shen , Matthew Zhang

One of the yet unsolved questions of QCD in the context of the Standard Model is to explain the strong CP problem. A way to look for a better understanding of it is to investigate the theory in the presence of a non-zero topological theta…

High Energy Physics - Lattice · Physics 2014-11-05 Lorenzo Bongiovanni , Gert Aarts , Erhard Seiler , Denes Sexty

We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various…

High Energy Physics - Lattice · Physics 2010-04-14 Gert Aarts , Erhard Seiler , Ion-Olimpiu Stamatescu

In the landscape of approaches toward the simulation of Lattice Models with complex action the Complex Langevin (CL) appears as a straightforward method with a simple, well defined setup. Its applicability, however, is controlled by certain…

High Energy Physics - Lattice · Physics 2018-04-18 Gert Aarts , Kirill Boguslavski , Manuel Scherzer , Erhard Seiler , Dénes Sexty , Ion-Olimpiu Stamatescu

Statistical sampling with the complex Langevin (CL) equation is applied to (0+1)-dimensional Thirring model, and its uniform-field variant, at finite fermion chemical potential $\mu$. The CL simulation reproduces a crossover behavior which…

High Energy Physics - Lattice · Physics 2017-10-25 Hirotsugu Fujii , Syo Kamata , Yoshio Kikukawa

Minimum-weight perfect matching (MWPM) has been been the primary classical algorithm for error correction in the surface code, since it is of low runtime complexity and achieves relatively low logical error rates [Phys. Rev. Lett. 108,…

Quantum Physics · Physics 2014-02-20 Adrian Hutter , James R. Wootton , Daniel Loss