Related papers: Optimizing the diffusion coefficient of overdamped…
In Stochastic Thermodynamics, heat is a random variable with a probability distribution associated. Studies of the distribution of heat are mostly in the overdamped regime and in one dimension. Here we solve the heat distribution in the…
We investigate the dynamics of an overdamped Brownian particle moving in a washboard potential with space dependent friction coefficient. Analytical expressions have been obtained for current and diffusion coefficient. We show that the…
We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a…
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…
We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…
Bayesian methods of sampling from a posterior distribution are becoming increasingly popular due to their ability to precisely display the uncertainty of a model fit. Classical methods based on iterative random sampling and posterior…
We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on the diffusion coefficient, we employ a…
We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…
Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject…
The randomized midpoint method, proposed by [SL19], has emerged as an optimal discretization procedure for simulating the continuous time Langevin diffusions. Focusing on the case of strong-convex and smooth potentials, in this paper, we…
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…
Sampling from constrained statistical distributions is a fundamental task in various fields including Bayesian statistics, computational chemistry, and statistical physics. This article considers the cases where the constrained distribution…
Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
For sampling from a log-concave density, we study implicit integrators resulting from $\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the…
We study zero-shot conditional sampling with pretrained diffusion models for linear inverse problems, including inpainting and super-resolution. In these problems, the observation determines only part of the unknown signal. The remaining…
We consider a class of stochastic control problems which has been widely used in optimal foraging theory. The state processes have two distinct dynamics, characterized by two pairs of drift and diffusion coefficients, depending on whether…
The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time…
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…