Related papers: Sampling and estimation on manifolds using the Lan…
We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method…
We introduce a scheme for deriving an optimally-parametrised Langevin dynamics of few collective variables from data generated in molecular dynamics simulations. The drift and the position-dependent diffusion profiles governing the Langevin…
Standard first-order Langevin algorithms such as the unadjusted Langevin algorithm (ULA) are obtained by discretizing the Langevin diffusion and are widely used for sampling in machine learning because they scale to high dimensions and…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
For a given target density, there exist an infinite number of diffusion processes which are ergodic with respect to this density. As observed in a number of papers, samplers based on nonreversible diffusion processes can significantly…
We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…
A model has two main aims: predicting the behavior of a physical system and understanding its nature, that is how it works, at some desired level of abstraction. A promising recent approach to model building consists in deriving a…
We introduce a numerical method for Brownian dynamics with position dependent diffusion tensor which is second order accurate for sampling the invariant measure while requiring only one force evaluation per timestep. Analysis of the…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
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…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…
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…
The paper addresses a problem of sampling discretization of integral norms of elements of finite-dimensional subspaces satisfying some conditions. We prove sampling discretization results under a standard assumption formulated in terms of…
We study the problem of sampling from a probability distribution $\pi$ on $\rset^d$ which has a density \wrt\ the Lebesgue measure known up to a normalization factor $x \mapsto \rme^{-U(x)} / \int_{\rset^d} \rme^{-U(y)} \rmd y$. We analyze…
We provide a numerical algorithm for the model characterizing anomalous diffusion in expanding media, which is derived in [F. Le Vot, E. Abad, and S. B. Yuste, Phys. Rev. E {\bf96} (2017) 032117]. The Sobolev regularity for the equation is…
We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…
Diffusions are a fundamental class of models in many fields, including finance, engineering, and biology. Simulating diffusions is challenging as their sample paths are infinite-dimensional and their transition functions are typically…
Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
We prove concentration inequalities and associated PAC bounds for continuous- and discrete-time additive functionals for possibly unbounded functions of multivariate, nonreversible diffusion processes. Our analysis relies on an approach via…