Related papers: Fast Convergence for Langevin Diffusion with Manif…
1. The utilisation distribution describes the relative probability of use of a spatial unit by an animal. It is natural to think of it as the long-term consequence of the animal's short-term movement decisions: it is the accumulation of…
We propose a computationally efficient random walk on a convex body which rapidly mixes and closely tracks a time-varying log-concave distribution. We develop general theoretical guarantees on the required number of steps; this number can…
Diffusion models are state-of-the-art methods in generative modeling when samples from a target probability distribution are available, and can be efficiently sampled, using score matching to estimate score vectors guiding a Langevin…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
Sampling from probability distributions of the form $\sigma \propto e^{-\beta V}$, where $V$ is a continuous potential, is a fundamental task across physics, chemistry, biology, computer science, and statistics. However, when $V$ is…
We study the mixing time of two popular discrete-time Markov chains in continuous space, the Unadjusted Langevin Algorithm and the Proximal Sampler, which are discretizations of the Langevin dynamics. We extend mixing time analyses for…
Langevin diffusion is a powerful method for nonconvex optimization, which enables the escape from local minima by injecting noise into the gradient. In particular, the temperature parameter controlling the noise level gives rise to a…
This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…
The mean-field Langevin dynamics (MFLD) is a nonlinear generalization of the Langevin dynamics that incorporates a distribution-dependent drift, and it naturally arises from the optimization of two-layer neural networks via (noisy) gradient…
As an example of the nonlinear Fokker-Planck equation, the mean field Langevin dynamics recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide neural networks in the mean field regime, and hence the…
It is well known that adding any skew symmetric matrix to the gradient of Langevin dynamics algorithm results in a non-reversible diffusion with improved convergence rate. This paper presents a gradient algorithm to adaptively optimize the…
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…
As a highly expressive generative model, diffusion models have demonstrated exceptional success across various domains, including image generation, natural language processing, and combinatorial optimization. However, as data distributions…
The Langevin Markov chain algorithms are widely deployed methods to sample from distributions in challenging high-dimensional and non-convex statistics and machine learning applications. Despite this, current bounds for the Langevin…
Continuous time random walks and Langevin equations are two classes of stochastic models for describing the dynamics of particles in the natural world. While some of the processes can be conveniently characterized by both of them, more…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Analysis of a Bayesian mixture model for the Matrix Langevin distribution on the Stiefel manifold is presented. The model exploits a particular parametrization of the Matrix Langevin distribution, various aspects of which are elaborated on.…
Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…
The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…