相关论文: Speeding up Langevin Dynamics by Mixing

The Metropolis-Adjusted Langevin Algorithm (MALA) is a Markov Chain Monte Carlo method which creates a Markov chain reversible with respect to a given target distribution, pi^N, with Lebesgue density on R^N; it can hence be used to…

We study the Langevin dynamics of diffusive particles with regular pairwise interactions under mean-field scaling. By approximating empirical distributions with conditional distributions, we establish coercive and contractive properties for…

We study the small-mass (overdamped) limit of Langevin equations for a particle in a potential and/or magnetic field with matrix-valued and state-dependent drift and diffusion. We utilize a bootstrapping argument to derive a hierarchy of…

We consider Adaptively Restrained Langevin dynamics, in which the kinetic energy function vanishes for small velocities. Properly parameterized, this dynamics makes it possible to reduce the computational complexity of updating…

Metastable transitions in Langevin dynamics can exhibit rich behaviors that are markedly different from its overdamped limit. In addition to local alterations of the transition path geometry, more fundamental global changes may exist. For…

We study the long-time behavior of the underdamped Langevin dynamics, in the case of so-called \emph{weak confinement}. Indeed, any $\mathrm{L}^\infty$ distribution (in position and velocity) relaxes to equilibrium over time, and we…

We propose a reflection-free Langevin framework for sampling and optimization on compact polyhedra. The method is based on the inverse Hessian of the logarithmic barrier, which defines a Dikin--Langevin diffusion whose drift and noise adapt…

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…

The classical (overdamped) Langevin dynamics provide a natural algorithm for sampling from its invariant measure, which uniquely minimizes an energy functional over the space of probability measures, and which concentrates around the…

Underdamped Langevin Monte Carlo (ULMC) is an algorithm used to sample from unnormalized densities by leveraging the momentum of a particle moving in a potential well. We provide a novel analysis of ULMC, motivated by two central questions:…

Explicit, momentum-based dynamics for optimizing functions defined on Lie groups was recently constructed, based on techniques such as variational optimization and left trivialization. We appropriately add tractable noise to the…

While systems analysis has been studied for decades in the context of control theory, it has only been recently used to improve the convergence of Denoising Diffusion Probabilistic Models. This work describes a novel improvement to Third-…

Let 0<\alpha<1/2. We show that the mixing time of a continuous-time reversible Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of stationary measure at least \alpha of the state space.…

Drift analysis aims at translating the expected progress of an evolutionary algorithm (or more generally, a random process) into a probabilistic guarantee on its run time (hitting time). So far, drift arguments have been successfully…

A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte…

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…

We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic…

Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is…

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long…

We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating…